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Un des symboles suivants apparaftra sur la derniire image de cheque microfiche, selon le cas: le symbole ~*> signifie "A SUIVRE ", le symbole V signifie "FIN ". Maps, platea, charts, etc., may be filmed at different reduction ratios. Those too large to be entirely included in one exposure are filmed beginning in the upper left hand corner, left to right and top to bottom, as many frames as required. The following diagrams illustrate the method: Les cartes, planches, tableaux, etc., peuvent dtre filmte 6 des taux de rMuction diffdrents. Lorsque le document est trop grand pour dtie reproduit en un seul cliche, il est filmA 6 partir da Tangle supirieur gauche, de gauche i droite, et d« haut en bas, en prenant le nombre d'images n^cessaire. Les diagrammes suivants illustrent la methods. rrata o )eiure, D 32X 1 2 3 1 2 3 4 5 6 ELE J Go:^vii J TH I IMUx (^' Co.'s ^bucational Series. ELEMENTARY HYDROSTATICS FA' , J. HAMBLIN SMITH, M.A., GONVILLE AND CAIUS OOLLllGE.. AND LATE LECTURER AT ST. Peter's college, Cambridge. J THIRD CANADIAN COPYRIGHT EDITION. Authorized by the Minister of Education. PRICB 73 CENTS. TORONTO : ADAM MILLER & CO., 1879. Entered acoordir : to Act o. PavUament o, Canada, in the year 1876. by ADAM MILLER & CO., In me Office of the Minister of Agriculture. r&?^7 \ I *v by PREFACE The Elements oi Hydrostatics seem capable «jf bein^ presented in a simpler form than that in which they appear in all the works on the subject \nth which I aai acquaintpd. I have therefore attempted to give a simple explanation of the Mathematical Theory of Hydrostatics H.nd the practical application of it. Prior to the publication of this work some copies w^ere privately circulated with a view to obtain opinions from Teachers of experience as to the sutliciency and accuracy of the inforaiation contained in it. A few suggestions received in consequence of this arrangement will be found in the Notes at ihe end of the volume. I am indebted to several friends for the collection of Miscellaneous Examples given in Chapter vill. In conclusion I have to expiess my thanks for the favour with which my attemptt^ to simplify the course of Elemen- tary Mathematics have been received by College Tutors and Masters in Schuols. J. HAMBLIN SMITH. Cambridge, 1870. CONTEXTS i .. ClIArTEli I. ViQS On Fluid Pkessoue 1 CHAP i'Eli 11. On the Puessuue of a Fluid aoti;d ox by (Iuavitt . 11 CHAi'TER III. On Specifio Guavixy 20 CHAPTER iV. On the Conditions of Equiliiuhum oi' Bodtks undeb tue Action of Fluids '>!' CHAPTER V. On the Propeijties of Air ...««. bw CHAPTER VI. On the Application of Air , . • • q • 6G CiiAPJ ER Vll. On the Theujiometeu 77 CHAPTER \'III. Miscellaneous Examples . . . . . • • 83 Answers . ..•••••* ^^ HYDROSTATICS. CHAPTER I. On Fluid Pressure, t 1. Hydrostatics was originally, as the namo imports, the sciouco which treated of tho P]quilibriiiia of Fluids, or of bodies in equilibrium mider tho action of forces some of which arc produced by tho action of fluids. It is now ex- tended so as to include many other theorems relating to the properties of fluids. 2. A fluid is a substance whose parts yield to any force impressed on it, avd by yielding are easily moved among themselves. 3. This definition 8ci)arates fluids from rigid bodies, in which the particles cannot be moved among each other by any force, however great, but it does not se|)arate fluids from powders, such as flour, in which wo have a collection of particles which can bo moved among themselves by tho appli iiation of a slight force. 4. A fluid difl'ers from a powder in this way : the particles composing a powder do not move among themselves "withou*- friction, whereas the particles that make up a fluid move one over another without any friction. For example, if you empty a mug of flour on a table the friction between tho particles will soon bring the flour to rest m more or less of a heap; whereas if you empty a nmg of water the particles, moving without friction, run in all direc- tions, and the wholo body of vratcr is spread out into a very fchiu sheet. a u. 1 aV FLUID PRESSURE. 5. To <listingiiish fluiils tVtuii |»ow(lors wo must thoroforo make nil ail.lili(»ii to Art. -J, uiiU \no y;ivo tlio follit-viiig a^ a coinplcto dclinition of a (laid. l)i;t'. A Jlaid is a ^uhdance vhone jxirlx yield to any f^rco imprc'sscd on it, and /'// yicldiiKj are Cdsdy mnjed ainnng Ihetnsclces without /rii'f.ion, and (dso (H't without /fiction on aiii/ aiir/aco with which they are in contuct. This dclinition includes nut only tlio bodies to which iu ordinary convoivsation wo apply the tonns "lliiid"and "liquid," such aH watci-, oil, .ind mercury, but also such bcilios as air, gas and steam. G. Fluids may bo conveniently diviiieil into two chussob, liquid and (jiiscous. JJy tho tevnj liquid we understand an incompres.sible and inelastic Ihiid. In reality nil tluids with which wo are a(.(iuainted aro c<»mpressible, that is, a given voluii;0 of iluid can by pressure be reduced in volume. Still 80 great a force i.s rccpiired to compress to any a]»prcciablc extent such lluids as water and mercury, that wo may regard them as incompressible in treating of tho elements of tho subject. 7. Tho inela.stie tluids with which wo are la-uitieally acquainted api)roach more or less to a Ktato of perfect lluidity, but in all there is a tendency, greater or less, of adjacent pa<'ticles to cohere with each other. This tendency is stronger in such fluids as oil, varnihh and melted glass, than in such as water and mercui-y. Hence tho former are called im^hrject or <'."."i>v."n/w (liiids. 8. The ail* which wo breathe and gases aro compressible fluids, and aro en<lowcd with a i)eifect elasticity, so that they can change their shape and volume by compres>ion, and when he compressi(m ceases they can return to their former shapo jid volume. 9. Vapours, as steam, are elastic lluids, but with this pc(,'uliarity: at a given tempcratiu'o in a given spice only a certain quantity of vapour can be contained, and if tho space or the temi)erature bo then diminisheJ, a portion of tho vapour becomes liquid, or even in some cases a soliil. 10. Before proceeding further with our subject wo nmst explain tho meaning of some technical terms which wo sliull have to employ frequently. 1 i ON FLUID PRESSURE. 11. A I'lstoii is a short cyliiulor of wood or motul, wliicli lits exactly tliu Citvity of niii;tlicr cyliiiUor, uuJ works* Uj^* uml down uUcniiitt'ly. VI. A Viilvo is u closud lid ullixud to tho end of a tubo or holo in a piston, opon- iiig into or out of si vessel, l>y niouiia of n hin{^o or otliur sort of inovjublo joint, in sucli a manner that it can be opened only in one direction. 13. A Prism is a solid flfjiiro, tlio ends of wliich are parallel eipial andsiinlliir pluno fi^'nres, and tho sides which connect tho ends ure parallelograms. Tho figure represents a rectangular prism, in which each of tho linos bounding tho surfaces of the i)ri8m is at right angles to each of the four lines which it meets. \ \ \ \ V 1 i 14. Wo shall often have to use tho expression Ilorizontai Section of a tube or hollow cylinder, and wo may explaiu tho moaning of the exprcssifm by the following example: Suppose a gun-barrel to bo placed in a vertical po.*iition: suppose a wad to be part of tho way down tho l^arrcl with its upper 8u. face exactly {)arallel to the top of tho barrel: tiicn BUi>pose the barrel to bo cnt away so as just to leave tho upper surface of tho wad exposed : the area of this surface of tho wad is called tho horizontal section of the barrel. 15. Tlio mathematical theory of Hydrostatics is found e>i Oil two laws, which weshidl now explain. ON FLUID PRESSURE, ^ 16. Law 1. The force exerted hij ajiidd on any surface^ Xiilli which it is in contact, is perpendicular to that surface. 17. This law is merely a rei)etition of the defmition of a fluid given in Art. 5, and wo can best explain its n'caniug and applicutic»)i by an examplo. li AB bo a cylinder immersed in a tlaid tlio pressures of the fluid on the curved Hurface are all perpendicular to the axis of the cylinder, and the pressure;, of the fluid on the flat ends are all parallel to the axis. Now It is a law of Statics that a fcrcc haa no tendency to produce motion in a direction perpendicular to its own direction. Hence the pressures on the curved surface have no tend- ency to produce motion in the (hrection of the axis, and the pressures on the flat ends have no tendency to produce motion •n a directioti perpendicular to ihe axis. ^ la Law il. Any pressure commjmicafed to the surface oj ajiuid IS equally transmitted through the whole jluld in every direction. ^. A characteristic property of fluids which distinLruishcs them from sclid iKKli.s is this faculty wjjich they possess of |:ransmittn.ir equally !d all dirccliona the pressuies upphod to their sm-luces. h 11 ON FLUID PRESSURE, 5 It is of great irnpoil .iice to form a con*ect notion of the priuciplo of "tho equal transinission of proMSuro," a priuciple wliicli is applicable to all fluids, inasmuch as it depends upon a property which is essential to all fluids and is not an acci- dental property, as weight, coloui-, and others. 20. Suppose then t^c take a vessel A BCD, in tho form of a hollow rectangular prism, uad place it on a horizontal table. Place a block of wood, cut to fit tho vessel, so that it rests on tho base BO and reaches up to the level EF. i Then if we place a weight P on the t('p of the block an additional pvcssuro P will be imposed on the base of the prism. Now suppose the block to bo removed and the vessel filled with an incouipressiblo fluid up to the level o^ EF. Suppose a piston exactly fitting the vessel to be inserted and a pressure P applied by means of it to the surface of the fluid at EF. In this case tho pretaure P is transmitted by moiuis of the fluid n()t oidy to the base BO, but also to the sides of the vessel, and if wo take a unit ot" area, as a square iiich, in the side FO, and a unit of area in the base BO, tlio same additional pre.-i- Buro will be conveyed to each. aV FLUID PRESSURE. •21. That jlalda tratismil pressure equally in all direc- iiu/is maybe sheicn ccpcrimevlally in IheJ'ulloiciug iiianner: ABC is a vessel of any sliape filled with fluid. SLiko openings of equal area at A, B, C. Close the ojieuings by pistons, kept at rest by such a forcd as may be required in each case. Then it will be found that if any addilional Coixe P be applied to the piston at A, the same force P must be api)nod to each of the pistons at B and (7 to prevent them from being thrust out. If the area of the base of one of the pistons, as B, be larger than the area of the base of the piston //, it is found that the pressure which niust be applied to B to keej) it at rest bears the same relation to the pressure applied to A tbiit the area of the base of B bears to the area of ihe base of A. 22. From the preceding article it is clear that if a body of fluid, supposed to be without weight, be confined in a closed vessel, the pressure connnunicated to the fluid by any area in any part of the vessel will be transmitted equally to every equal area in any other part of the vessel. It is owing to this fact that the use of a Safety Valve can bo depended <ju. / f i pi! 1 ]"" iiil i ii "1 \ 1 i] , ii i '•II 1!' 1 ' 1 1 1 1 1 : li i i ii ii i H 1 i alii. ill ! i- ii 1 ill :4 ill 111 ,11 il 1 i ! 1 ! 1 ; 1 m \ t 1 ' I E * a V s i 'ec- OX FLUID PRESSURE. Thus, if tho vessel A be full of steam and the pressuro of the steam be required to be kept down to 200 lbs. on the square inch, if a valve B, whose area is a square mch, be placed at any part of the vessel, and be so loaded that it will require a force of 200 lbs. to raise it, then if the steam acquire an increase of pressure above '200 lbs. on the square inch, the valve vaW open, and will remain open till tho pressure of the steam is just equal to 200 lbs. on the squai-e nicli. 03 Any force, hcicever small, may by the transmission of "its pressure through a fluid, he made to support any weight, however large. red tif :he nd ^er :ho irs •ea D F. Ti ' 11 ii wmmmrnM i;;lliil|nii!|!iil iilM !iili!!ii!ir liMMiiliiiiij F of led hi Mi i Snppose DE and FH to be two vertical cylinders, con- nected by a pipe EH, and suppose FH to have a homontal section much larger than the horizontal section of DE: tor instance, let the area of a horizontal section ot / ^ be 400 square inches, and the area of a horizontal section a Dh bo 1 square inch. -a Now if water be poured into tho cylinders, and pistons A and n be applied to the surface at D and /; wlKitcvcr force we apply to A will be transmitted to each portion of the base of the i)istou D which is equal in area to the base of the piston A. , . , A -u Hence a pressure of lib. applied to the piston A will pro- duce a pressure of 400 lbs. ol tlio base of the piston B, and ^vill therefore support a weight of 400 lbs. placed on the ^^^ This elTcct of pressure by tho medium of a fiuid is often called Tho Hydrostatic Paradox. ON FLUID PRESSURE, Examples. — I. (1) In the experiment described in Art. 23, if the horizontal section of the small cylinder bo \\ square inches, and that of the larger cylinder 61 sq. in., find the weight supported under a pressure of 1 ton exerted on the piston of the small cylinder. (2) If the horizontal section of the small cylinder be \\ square inches, and that of the large cylinder 240 sq. in., find the weight supported by a pressui'O of 3 cwt. applied to the piston of the small cylinder. (3) If the pistons are circular, the diameters being l^^ inch and 50 inches, find the weight sup'ported by a pressure of 15 lbs. applied to the smaller piston. (N.B. The areas of circles are as the squares of tlieir diameters.) (4) A closed vessel full of fluid, with its upper surface horizontal, has a weak part in its upper surface not capable of bearing a pressure of more than 4^ pounds on the square foot. If a piston, the area of which is 2 square inches, be fitted into an aperture in the upper surface, what pressure applied to it will burst the vessel ? • (5) A filosed vessel full of fluid, with its upper surface horizontal, has a weak part in its upi)er surface not capable of bearing a pressure of more than 9 lbs. upon the square foot. If a piston, the area of which is one square inch, bo fitted into an aperture in the upper surface, what pressure applied to it will burst the vessel ? i 4 \ (6) If the horizontal section of the small cylinder be \\ square inches, and the diameter of the large piston 20 inches, find the lifting power of the machine under a pressure of I ton exerted on the piston of the small tube. (N.B. The area of 22 a circle is — times the squire of the radius nearly.) I ON FLUID PRESSURE. 24. The pressure at any point in any direction in a fluid is a conventional expression used to denote tlie presauro on a unit of area imagined as containing the point, and ijcrpendicu- lar to the direction in question. Per examphj, if the whole pressure of a fluid on the bottom of a vessel is 2000 lbs., and the pressure is uniform throughout, then if we take a square in(;h as the unit of area, and the area of the bottom of the vessel is 40 square inches. the pressure at a point in the base is -- lbs. or 50 lbs. 25. The student must carefully observe the distinction between the expressions "pressure on a point" and "pressure at a point" : the former is zero, because a point has no magnitude. 26. If a mass of fluid is at rest, any portion of it may bo supposed to become rigid without affecting the conditions of equilibrium. Thus if we consider any portion A of the fluid in a closed vessel, we may suppose the fluid in A to become solid, while the rest of the fluid remains in a fluid state, or w^e may suppose the fluid round A to become solid, while the fluid in A remains in a fluid state. I I 27. The importance of the principle laid do^vn in the pre- ceding article may be seen from the following considerations. The laws of Statics are proved only in the case of forces acting on rigid bodies. Now since the supposition of any part of a fluid becoming solid docs not affect t^e action of the forces acting upon it, and since we can in thac jase obtain the effect of tlioso forces by the laws of Statics, we shall know their effect on the fluid. [O ox FLUID PRESSURE. 28. If a body of fluid, supposed to bo witliout weight, b« confinod in a closed vessel, so a.s to cxuctly till the vessel, an equal [Ji-essure «''ill be exeited on the fluid by every ecpial area in the sides of the vessel (Art. 22), and wo proceed to shew tiiat the pressure is the same in all directions at every point of the fluid. For let be any point in the iluid, and AB, CD two plane surfaces, each representing a unit of area, passing through O and parallel to two sides of the vessel EF, GH. Then drawing straight linos at right angles to AB, CD from the extremities of AB, CD to tho sides of the vessel, we may imagine all the tluid except that contained in tho prism ABNM to become solid. Then tho pressure exerted on tho fluid by the area MN will be transmitted tf) AB. Again, if we suppose all tho fluid except that contained in the prism CDSR to become solid, the pressure exerted on the fluid by tho area RS will be transmitted to CD. Now the pressures exerted on tho fluid by the areas MN, RS are equal, and consequently tho pressures on AB, CD mil be equal, that is, the pressure at the point O is the same in all directions. Also since the distance of the point fi am the sides of the vessel is not involved in tho preceding considerations, it follows that the pressure is tho same at every point ^ CHATTKR H. On the Press7ire of a Fluid acted on by Gravity. 29. In tlie preceding chiix>ter we considered tlie conse- quences thiit result from the peculiar property, essential to all fluids, of transmitting equally in all directions the pressures applied to their surfaces. We have now to considor the effects produced by the action of gramty upon the suhstavrf of a fluid. 30. The stiulent must mark carefully the distinction be- tween force ap[»lied to a surface and force applied to each of the particles composing a body. As an example of these distinct forces consider the case of a book resting on a table. F(U'ce is applied to the surface of the book by the table, and thus is counterbai<Luced the force of gravity which acts upon each particle of uiiich the l»()ok is composed. 31. All fluids are subject to the action of gravity in tlio name way as solid bodies. Viach ]>arti(:le of a fluid has si tendency to fall to the sm-face of the earth, and in a mass of fluid at rest there is a particular point, called the centre of gravity, at which the resultant of all the forces exercised by the attrac- tion of the Earth on the particles composing the fluid may be supi)osed to act, 32. The term density is applied to fluids, as it is to solid bodies, to denote the degree of closeness with which the pai-ti c'es are packed. !i a w ra OM TTTK PRESSURE OF A FLUID Wlien wc speak of a fluid of /c,«(/(jrm density, \v(3mcan that if from any part of tlie l)ody of lluid a portion be t;ikon, and if from any other part of tlio body of fluid n jjortion like in form and equal in vohnno to the tovnier portion bo taken, the weights of the two portions will bo e(inaL 33, If a vessel bo filled with a hoa^7 fluid of uniform density the pressure at every point in tlie interior of the fluid will not bo the same, because the pressure which results from the action of gravity will v.ary in magnitude according to the position of the point m the contai'ihig ve'^scl. Consider a closed surface of small dimensions containing the point A , and snpjioso the fluid outside the closed surface to become solid. The fluid icithin the closed surface will exercise pressure against the surface at evci-y point, and these liressures will 1)0 unequal, because the fluid is acted on by gravity. But we may conceive that, if the (piantity of fluid within the surface be cern umall^ the diflerence between the pressui-es at diflercnt points of the suiface will be very small, and when the surface is indefinitely diminished the pressures exercised by the fluid at each point of the surface may be regarded as equal, and the weiglit of the fluid may be neglected. Thus wo can consider it as the case of a weightless fluid and apply the conclusions of Art. "28. Hence all the planes of equal area which can ho drawn, passing through the point A and not extending beyond fJie small surface, may be considered to be subject to equal presHuros. pa va; de th( pU th( -« de th( po ACTED ON BY Gh'A VfTY. n 80 wc conclude that in a heavy fluid of uniform density (1) Tho pressure will vary from point to point. (2) Tl»e pressure will bo tho same in all dirccLionn at any particular point. 34. Wo have next to consider in what way the pressure varies from point to i)oint in the interior of a (luid (tf luiiform density when it is in equilibrium, and (irst we shall shew that the pressure is the mnie at all points in the same horizontal plane. Let A and B be two points in the same horizontal plane in tho interior of a fluid of uniform density. ■•■■*, I Imagine all the fluid contained in a small horizontal cylin- der, of which AB \^ the axis, to become solid. Then tho forces actinj' on the cylinder are t pan allel to tho axis (1) The fluid pressures on its curved surface) perpendicular (2) The weight of ihe cylinder j to tiie axis. (:>) The fluid pressure on the end A (4) The fluid pressure on the end B\ Of these (1) and (2) have no tendency to produce motion in the direction of tho axis (Art. 1 7). Therefore, since there is tio hon/,»mtaJ motion, fluid pressure on end A = fluid pressure on end B. And since, the ends being very small, the pressure at every point in each end may bo regarded as the same, prcssm-G at point A = pressure at point B. \. i 14 ON THE PHKSSURE OF A FLUID or*. The pressure at auj/ point vithin a hmvy inelnslie ffaid, not e^rposed to externa/ presxxro, is ]>rnp(,rtioual to the depth of that point below the surface of the fltiiiL A Ji =1^ ■". ■ — ~_:^z:zr^ — 1_ ■ - m . ^ ^-*^^ . , — ~ __ 1 — : V ' — "' -'■■■- - J'^ ■ — '-^:r:s:^— I Let P and Q be two points at difFercnt rloptha below the surface of tlio fluid. Suppose two small equal and liorizontal circles to bo described round P and Q as centres. Then suppose the fluid in the two small vertical cylinders PA, QB, extending from tlio bases P and Q to the surface, to become solid. Now tlie forces acting on the cylinder PA are (1) The fluid pressures o\\ its curved surface, all of which are perpendicular to the axis. (2) The wciglit of the cylinder ) (3) The fluid pressure on the base p\ P^''''"'^ *^ ^^'' '''^^^ Of these (1) lias no tendency to produce motion in the direction of the axis (Art. 17). Hence since there is no vertical motion, fluid pressure on base /* = weight of cylinder PA. So also, fluid pressure on base Q = weight of cylinder QB. Ilenco pressure at point P : pressure at point Q :: pressure on base P. pressure on base Q, (Art. 24.) :: weight of cylinder PA : weight of cylinder QB, :: length of PA : length of Qi?(lhe bases being equal), ::depthofP :depLh of (^. Cor. If pressure at P = i)ressure at Q depth of P^ depth of ^. ACTED ON BY GRAVITY. n . Tho pressure of the iitinospheio on the 8urf;ico of tho fluid is not taken into account, but we Hhall shew liL-reafter how it aUocts the pressure at a point in tho interior of a fluid. 3(5. TIm surface o/ a heaoy inelaslic jluUl at rest U horizontal.. i^)oz:-i::F=- Let A and B bo two points in tho same horizontal plan in tlie interior t»f a heavy fluid at rest. Suppose the iiuid contained in a small horizontal cylinder uf fluid, of which ABh the axis, to become solid. Then, fluid i)ressuro on cud A = fluid pressure on end B (Art. 34), and, since the ends are equal, fluid pressure at point A = fluid pressure at point B Hence A and /; are at tho same <lepth below the surface of tho fluid (Cor. Art. 35), and if we draw AC, Z?Z> vertically to meet the surface in (7, Z>, AC=BD, also, ^C is parallel to BD ; .-. CD is parallel io AB (End. i. 33) • . . CD is horizontal. Similarly any other point in the surface may be proved to be in the same liorizontal plane with C or Z> ; .•. tho surface is horizontal. 37. The proposition thai the surface of a fluid at rest is horizontal is only true when a very moderate extent of surface is t-\ken. Larj^e surfaces of water assume, in consequence ol the ati>i'au tion exercised bv the earth, a spherical form= i6 ON THE PRESSURE OF A fLUID The following practical msults aro worthy of notice : (1) All lluids (iiid thoir lovol. If tiiboH of vurioua shapes, Boiuo largo uiul sonio Hinall, soino Htraii,'ht uu«l oiliorH bent, bo placed in a closed vessel full of wjiter, iind water be tlieii poured into one of the tubes, the lluid will rwe to a uniform height in it and all the other tubes. (2) It pipea bo laid down Ironi a reservoir to any distance, the tluid will mount to the same height as that to which it is raised in the reservoir. • (3) The suiface jf a lluid at rest furnishes a means kA observing objects at a distance in the same horizontal plane with a mark at the place of observation. 38. Wo have seen that in an inelastic lluid at rest the pressure at any point depends on the depth of that point below the surface of the lluid, that is, on tl-e lengUi ot the vertical lino ilrawn from the [)uint to meet ii horiznntal lim drawn througli the highest point in the fluid. Thus if ABO be a conical vessel with a horizontal base, standing on a table, and lilled with fluid, the jjressure at any point P is determined in the following manner. r. 1 ii From yl, the highest point of the fluid, draw a vertical lii] j meeting the horizontal plane passing through P in the point <;> Then the pressure at /» = pressure at Q, because P and Q, are in the same horizontal plane. But pressure of Q depends on the length of AQ; therefore pres.vr re "> P fleponds on the length of PR, a line drawn verticallv to i;;eei the horizontal line AR, ACTED ON BY GRAVITY. »7 39 If a te%9eU '\f ^hlch the hotfom u horizontal and {hemh's rerticd, he jUhd with Jlnid, thn pres>sure on Uu boUom will be equal to the weight q/'thejluid. Vlg. I. Fig. II. Fig. ni. Let ACDB (fig. I.) bo a vessel whoso bottom, CD, is hori- zontal, and its sides vertical. Wo may consider tho fluid in this vessel to bo niado up of vertical columns of fluid. Each ol tiiese columns will press vertically downwards with its weight, and the sum of these pressures will bo tho weight of tho fluid. Now tho base of the vessel, being horizontal, will sustain all those vertical pressures ; /. pressure on tho base of tho vessel = weight of the fluid. If tho sides of tho vessel be not vortical, as in figs. II. and III tho pressure on tho base will bo equal to tho weight of a column of fluid ECDF, EC and FD being perpendicular to CD, and EF being tho surface of tho fluid. Ileiico if in tho throe vessels tho bases aro equal and on the same horizontal plane, and tho fluid stands at tho same height in tho vessels, the pressure on tho base in each case will be tho same. The fluid in vessel I. produces a pressure on the base equal to its own weight. The fluid in vessel II. produces a pressure on the base less than its own weight. The fluid in vessel III. produces a pressure on the base greater than its own weight. i8 ON THE PRESSURE OF A FLUID EXA2 PLES.— IL (1) If the pressure at a depth of 32 feet 1)0 lo lbs. to the square inch, whi>t will the pressure be at a depth of 42 feet 6 inches ? (2) If the pressure at a depth of 8 feet be 14^ li'>s. to the square '.ucli, wiiat Avill bo the pressure at a depth of 20 ft. 6 in./ (3) III tv'o uniform fluirls the pressures are the same at the depths of 3 ahd 4 inches respectively : compare the pressures at the depths of 7 and 8 int les respectively. (4) In two uniform fluids the pressures are the tame at the depths of 2 and 3 inches respectively : compare tlie pressures at the depths of 9 and 12 inches respectively. (5)* Find the height of a column standing in water 30 feet deep, wheu the pressure at the bottom is to the pressure at the top as 3 to 2. (6) If the pressure of a uniform fluid, not exposed to external pressur',', bo 1 .5 lbs. to the square inch at a depth of 15 feet, what will be the pressure at a depth of 12 feet ? (7) If the pressure of a uniform fluid, not exposed to external pressure, bo 3 lbs. to the square inch at a depth of 4 feet, w!iat will be the pressure on a uquure inch at a depth of 12 feet? (8) What is the pressure on tlie horizontal bottom of a vessel filled with w^ater to the depth of 2^- feet, the area of the base being 20 square feet, antl the weight of a cubic foot of water 1000 oz. '\ (9) A cubic foot of mercury weighs 13G00 oz. Find the pressure on the horizontal base of a vessel containing mercur}, the area of the base being 8 square inches, and the depth of the mercury 3 inches. (10) What is the pressure on the horizontal base of a vessel filled with water to the depth of 15 feet, the area of the base being 24 square feet, and the weight of a cubic foot of water iOOO oz. ] (11) A cistern shaped like an equilateral triangle of which one side is fi feet is filled with water to the depth of two feet : find the pressure on the base, the weight of a cubic foot of water beiiii? 1000 oz. . f hi ACTED ON BY GRAVITY. 19 i J (12) The spout of a teapot springs from the middle point of one side, and its upper extremity is on a level with the lid. If tlie spout be broken oiY half-way, how high can the teapot bo filled ? (13) When bottles that have been sunk in deep .vater have been brought up, their corks have been found driven in. How do you explain this \ (U) If a pipe, wjose height above the bottom of a vessel is 112 feet, be inserted vertically in the vessel, and the whole be filled with water, find tlie pressure in tons on the bottom of the vessel, the :irea of the bottom being 4 square feet, and tlie weight of a cubic foot of water 1000 oz. (15) A hole, a square inch in area, is bored in the flat cover of a vessel full of wacer, and a smooth piston weighing 7 lbs. 13 oz. is fitted into it ; a vertical tube is then fitted into another hole in the cover, and water is poured iuto it: find how hi«-h the water must be made to ascend in it in order that the piston may be driven out, a cubic foot of water weighinij »,; «--2 ^ ; ?*ii I- I m *c CHAPTER III. Oh Specific Gravity. 40. Some substances are from the nature of their conn)o- sitioii more weighty than others. We call gold a heavier metal than lead, because we know by experience that a given volume of gold is more w eighty than an equal volume of lead. 41. Wo make a distinction between the terms weight and weightiness. We si;eak of the weight of a particular lump of gold or iron. We speak of the weightiness of gold or iron, not referring to any particular lump, but to the special characteristics of the metals in question. Further we say that gold is heavier than iron, having no particular lumv) of tlio metals in viovv, bnt expressing our notions of the degree of weightiness tliat is peculiar to either substance. This degree of weightiness is known by the name Specific Gravity. Def. The Specific Gi'avity of a suhstancc is the degree of weightiness of that substance. 42. If of two substances, one of which is twice as weighty as the other, we tidce two lumps of equal volume, the weight of one lump is evidently twice that of tlie other : and, generally, if one substance be /S' times as weighty as the other, the we'ght of any volume of the first is ,S' times the weight of an equal volume of the other. Now l>y a sulistuice, the measure of the specific ! ravity of which is aV, wo mean a substance which is S times as weighty as the standard by which specific gravities are estin)ated. Tiierefore any volume of this substance will weigh S times as much as the equal volume of the standaid. i ON SPEC I FTC OR A VITY. 21 i 43. Tho requisites for a Standard are that it should be definite and uniform, and these requisites are possessed by Pure Distilled Water at a certain temperature. This substance is therefore taken as the standard for estimating the specific gravities of solid bodies and inelastic fluids. 44. When we say that the specific gravity of gold is 19, we mean that tho specific gravity of gold is 19 times that of Pure Distilled Water, and therefore a given volume of gold weighs 19 times as much as the same volume of distilled water. 45. To measure the Weight of a body we must have a unit of weight, and to measure the Volume of a body we must have a unit' of volume. These units we may select in any way that may suit our purpose, and we connect them with the unit of specific gravity by the following convention : The unit of specific gracity is the specific gravity of that substance of which a unit of volume contains a unit of iccight. 46. To find the numerical relation existing between the measure of the specific gravAty of a substance and the mea- sures of the weight and volume of any given quantity of the substance. Let W represent the measure of the weight of a substance, that is the number of times it contains the unit of weight. Also, let V represent the measure of the volume of the substance, that is the number of times it contains the unit of volume. And let S represent the measure of the specific gravity of the substance, that is tho number of times it contains the unit of specific gravity. Then one unit of volume of this substance will weigh S times as much as a unit of volume of the standard substance, ^Art. 42) that is, its weight is 6' times the unit of weight. Therefore the weight of V units of volume is VS times the unit of weight ; therefore the mcusure of the weight of V units of volume of the substance is VS ; but tliis measure we have denoted by W\ • \V^ VS. r) i i;^!l .1 ■ St! f 22 ON SPECIFIC GRA VITY. 47. The equation W^ VS gives us merely the relation between three nunil)cr.s, and two of these must be given ii) order that .ve may determine the third. When we have found it we know the mm^/o-e of the weight or volume or specilic gravity, as the ease may be, and we must have the unit of weight, (,i of volume, or of s]),x-ific gravity aI«o given to enable us to determine the wei-ht or volume or specifie gravity of a partieular substance. So that we may mi it thus : i measure of weights VS, measure of volume - W »1. », •md JV measure of specific gravity = — ; weight = Fas' times (unit of weight), W volume = -^- times (unit of volume); TT7- .specific gravity = -p times (unit of specific gravity). ■ ■ 48. A cubic foot of pure distilled water at a temperature of 62« Fahrenheit weighs about 998 oz., and for rough calcula- tions it is assumed that the weight of a cubic foot of water is lOOO ounces. Then if we take 1 cubic foot as our unit of volume and pure distilled water as our standard of specific gravity the unit of weight will be 1000 ounces. Or if we prefer to take 1 lb. avoirdupois as our unit of weight and pure distilled water as our standard of specific gravity, the unit of volume will be j^-^ of a cubic foot, that ia OiG cub. ft. aV SPECIFTC GRA VITY. 23 H 1 49. We shiill next explain how quantities are mensiired ; and then we sliall give three examples, worked out first on tho supposition that 1 cubic foot is taken as the unit of volume, and secondly, on the supposition that 1 lb. avoirdupois is taken as the unit of weight, so that tho student may see that the same result must follow from both suppositions, and that such a choice may bo made as to the units as may be suitable to any particular case. 50. To measure any quantity we fix upon some definite quan- titv of the same khid for our standard, or unit, and then any quantity of that kind is measured by finding how many times it contains this unit, and this number of times is called tho measure of the quantity. For example, if one pound avoirdupois be the unit of weighty the measure of 16 lbs is 16. Or, to put our calculations in a tabular form, we may give the following Examples : "X., h s Unit. 1 lb. avoird. 1 lb. avoird. 1 lb. avoird. 1 cub. ft. 1 cub. ft. 1000 oz. av. •016 cub. ft. Quantity. 8 lbs. 4 oz. 1 lb. troy. 6^ cub. ft. 3 cub. in. 14 lbs. av. b cub. in. Measure. 8. 1 4* 5760 7000 * 6-5. .3 17-28 ' 14x IG 1000 • r728~)r Ole ' l€ ■ I '■ 24 ON SPECIFIC GRA VIT Y. 61. First, when 1 cubic foot is taken as the unit of volume, and consequently 1000 oz. as the unit of wciglit, to solve the following examples : Ex. (1) The specific gravity of load is ir4, find tho weight of 720 ciihic inches of lead. Hero r=/i«, 5=114. Weight required = VS (unit of weight) 720 \ ~ ( r2s ^ ^ ^ "^ ' ^^"^^^^ ^ ^"" ^^' = 4750 oz. Ml \ = 296 'lbs. o Ex. (2) If 5 cubic feet of a substance weigh 240 lbs., what is its specific gravity \ TT rjfr 240X16 ,^ ^ Here W= — — ^ , r= 5. iOOO w Sp. gr. required = v^ (unit of specific gravity) 240 X 16 — - - - (unit of specific gravity) 240x16 (unit of specific gravity) lUU0x5 = "768 (unit of specific gravity). Ex. (3) What is the volume of a substance whose specific gravity is 9*6 and whose weight is 4200 lbs. ? .. TT^ 4200x16 ^ ^ • Here^=-j^^,^ -,.9=9'6. Volume required == -v (unit of volume) 4200 X 16 1 000 : 7 cub. ft. culx ft. ^\ i ■^iE«ias*»«-»«»»««»'«-»«*«»' .-i^^g^^^ ^. .«■... -r ON SPECIFIC GRA VITY. 25 52. Secondly, when 1 lb. avoirdupois is taken as the unit of weight, and consequently '016 cub. ft. as the unit of volume, our examples will stand thus : ti ft Ex. (1) Here r= 720 172s X -016 , aS'=11-4. ^V^ eight required = VS (unit of weight) ~ X ^ X \\'^ times lib. 28 -016 / = 296 lbs, (5 'i Ex. (2) Here rF=240, V- W •01(j Sp. gr. required = 77 (unit of specific gravity) i,^h I 240 5 •016 (unit of specific gravity) 240 X 016 (unit of .specific gravii; 1 08 (unit of specific gravity). I Ex. (3) Hero W^=4200, *S'=9-6. W Volume required = -;t (unit of volume) 4200 ,. =; tmies WKy •016 cub. i^ 4200 9-() X xl6 1 000 cub. ft. ^ 7 cub .ft. m if f I i J1 J 1 ■1 ^ «6 gy SPECIFIC GKA V/TY. ^ f).']. If a iinniber of substances be put tojjctlier to form a mixture, wo shall gmerally have the following relations : (1) sum of measures of weights of compounds = measure of weight of mixture. (2) sum of measures of volumes of compounds = measure of volume of mixture. Thus if «<7i, w^, w^ bo the measures of the weights, ri, tv «?3, volumes, Sj, S2, s..j, specific gra- \aties of the compounds, and w, V, s the measures o^ the weight, volume and specific gravity of the mixture, we shall have Wi + Wj + '^'3 + -'^t i\-^i\^ + v.^+ =»; and therefore U'l ^2 w^ _w _ . -I_ — -f. -f".. — ""• h .'fl h « Note. We say that these relations hold generalbf, because in some cases, when substances nre mixed, tlie volume of the mixture is not equal to the sum of the volumes of the two substances. For instance, 70 pints of sulphuric acid mixed with 30 pints of water will make a mixture of less thaii ODphits. 54. In applying these formula; to the solution of examples, we may take any unit of volume or of weight, adhering to it through the whole cidculation. Ex. (1) To find the specific gravity <;f a mixed metal com- posed of 5 cubic inches of copper, specific gravity 9, and 8 cubic iaclies of tin, specific gravity 7'2. Since i\ s^ + v^ s^ — ??.<?, if wo take 1 cubic inch as the unit of volume, we ha e 5x9 + 8x7-2 = (5 + 8).9; ..*= — -,., - / "90 nearly 13 "' i ON SPECIFIC GRA VITY. 27 Ex. (2) Ten pfninds of fluid, specific jjravity I'Or), are mixed with 15 pouiuls of distilled water. Find the specific giavity of the niixturo. Since Wj w„ w -' + —-' = -, 1 2 * if we take 1 lb. as the unit of weight, wo Ikivo 10 15 25 1-05 1 5_5;15 •*'.9"l-05' 105x5 105 ,^,,^ , /. 8^ -— — -= -- -=roi9 nearly. 615 lu:{ •' 1^1 55. The Density of a substance is the degree of closeness cith which th^ 'particles composing the substance are packed "ogether. The difference between density and specific gravity may be stated thus : in estimating the density of a body we take into account the quantity of matter contained in a given volume : in estimating the specific gravity of a body we take into account the effect of the action of gravity on a given volume. If we cake t!ie same substance, as pure distilled water, as that to wdiich we refer as a standard in measuring the doi ^r>\ specific gravity of another substance, the mea? : the density and specific gravity will be the same. Examples. — III. 'M (1) The specific gravity of copper is 8"91 ; find the weight of 512 cubic inches of copper, a cubic foot of water weigliing 1000 oz, (2) If 4 cubic inches of iron weigh as much as 72 cubic inches of amber, compare the specific gravities of iron and amber. 'I |8 ON SPECIFIC OR A VITY. (3) Tho specific gravity of mercury being 13'3, find tho weight of one cubic inch of it, liiiving given that a cubic foot of water weighs 1000 oz. (4) If two cubic feet of a substance weigh 100 lbs., what is its specific gravity ? (5) Find tho weight of 36 cubic inches of cork, whoso specific gravity is 024. (6) A cubic foot of water weighs 1000 oz., what will bo the weight of a cubic inch of a substance whoso specific j^riivity is 3? (7) What is the specific gravity of a body of which m cubic feet weigh n lbs. 1 (8) Five cubic inches of iron weigh 22i oz., what is tho specific gravity of iron? (9) Twelve cubic feet of dried oak weigh 875 lbs., what is the specific gravity of the wood ] (10) Twenty-six cubic feet of ash weigh 137Hlbs., what is its specific gravity ? (11) A metal, whose specific gravity is 15, is mixed with half the volume of an alloy whose specific gravity is 12, find the specific gravity of the compound. (12) Two metals are combined into a lump the volume of which is 2 cubic inches ; ^ h cubic inches of one metal weigh as much as the lump, and 2J;r cubic inches of the other metal weigh the same. What volume of each of the two metals is there in the lump ? (13) • Two substances whose specific gravities are 1"5 and 3-0 are mixed together, and form a compound whose specific gravity is 2-5 ; compare the volumes and also the weights oi the two substances. (14) The specific gravity of sea-water being r027, wlmt proportion of fresh water must be added to a quantity of sea-water that the specific o-ravity of the compound may be 10091 I ON SPECIFIC GRAVITY. 29 and (15), Eqtial woijflits of two siibMtancos whoso densiUoH are 3'2r) and 2"75 arc mixed tojjcther ; find tlio density of the compound. (16) Equal vohnncs of two substances whoso specific gravities aro 25 and r5 are mixed to^jetiior; wliat is the specific gravity of the compound ] (17) Five cubic inclics of load, specific gravity irn5, aro mixed v.ith the same volume of tin, s[)ucific gravity 73; what is tlie specific gravity of the compound / (18) A mixture is formed of e<iual volumes of three fiuids ; the densities of two aro given and also the density of the mixture. What is tlio density of the third fluid? (19) Ten cubic inches of copper, sjiecific gravity 8'9, are mixed witli seven cubic inclies of tin, specific gravity 73 ; find tlio specific gravity of thy compound, (20)% Three fluids, wiioso specific gravities are 7, *8 and 9 respectively, are mixed in tlio proportion of 5 lbs., 6 lbs., and 7 lbs. What is tlie specific gravity of the mixture I (21) Tljo specific gravity of pure gold is l!)-3 and of copper 8'62 ; required the specific gravity of standard gold, which is a mixture of eleven parts of gold and one of copper. (22) When 6J1 pints of sulphuric acid, specific gravity 1*82, are mixed with 24 pints of water, the mixture contains only 86 pints, Wliat is its specific gravity \ (23) If three fluids the volumes of which are 4, 5, 6 and the specific gravities 2, 3, 4 are mixed togetlier, determine the specific gravity of the compound. (24)* The specific gravity of quartz is 2-62, and that of gold 19"35 ; a nugget of quartz and gold w^ciglis 115 oz., and its specific gravity is 7'43 ; find the weight of gold in it. (25)*» An iron spof n is gilded, and the mean specific gravity of the gilded spoon is 8; those of iron and gold are 7'8 and 1 9"4 : find tlio ratio of the volumes and weights of the metals employed. ■)::i i. ►• 'ii t:; CHAPTER IV. On the Conditions of Equilibrium of Bodies under the Action of Fluids. 5f). Wjimn a body is wholly or partially immersed in a fluid, it is a ^eiierMl priuciijlo of Hydrostatics that the. rmdtaiit. pressure oft/tejlidd on Ui.a snrfice of the hodij h cqntd to the weigid of the f aid dhplaeed. This principle \vu shall prove for two cases in Articles 57 and (jl. (l; When the body is icholly immersed in the fluid : (2) When the body is partially inn)ier,sed in the iluid. 57. To find the remdtant Pressure of a Fluid on a body y'hohy mi?ncrsed and foatinff in a fuid. ^ Lot A be a body floating in a fluid and wholly immersed . m it. ! the L fluid, ultaiif, to the prove lid. \ body M ON THE COrrPITIONS OF EQUHJnRIUM ^c, 3 1 Iiiuij^Mno tlio body roniovcd and tlio vae;mt Hpaco (illod uitlj fluid of tlio saiu(; idui as tliat in which tho hody floated. Tlien suppose this substituted fluid to become solid. Tho pressure at each point of its surfiico will still bo the Banio as it was at the same point of the surface of .4 Tho solidifled fluid is kept at rest by (1) Tho attvactio"! exercised by tho earth on every par- ticle of its mass : (2) Tho pressures exorcised by the fluid at tlio diflereut points of its surface. Ilonco the resultants of these two sets of forces must be eqmd in ma<jnitadc and ojjptjsilc in their lines of action. Now tho resultant of set (I) is called the weight of the solidified fluid and ;icts \cxW<^\Ac!j downwards througii its centre of gravity. Hence the resultant of set (2) is equal in magnitude to tho weight of tlie solidified fluid and acts veitically upicards through its centre of gravity. Now since the proL^sures on the solidified fluid are tho same as on tho body A, we see that the resultant pressure of tho fluid on A is eipial to the weight of the fluiil disj)laced by A and acts vertically upwards tlirough the centre of gravity of this ,disj)laced fluid This principle we shall now apply to tho following Ex- amples in ytatics. li 5rsed 58. Ex. I. Find tlie conditions of cqidUhrium of a body floating in afiiid and tcholly immersed in it. Tho body A (see diagram in Art. 57) is kept at rest by (1) Its weight, acting vertically downwards through its centr'> of gravity : (2; The pressures of the fluid on its surtacc, the resultant of which is equal to the weight of the fluid displaced by A and iicts vertically upwards through the centre of gravity of the fluid displaced. I .11 ► • I' hi 32 ,___S^^{^^^jCC^D£TJONS OF EQUILIBRIUM Hence (1) Weiglit of A - weight of fluid displaced by A : (2) The centres of gravity of ^ and of the fluid displaced are in the same vortical lino. These are the conditions of equilibrium. Note. A difiiculty often occurs with beginners in conceiving how a solid body can be in equilibrium in the midst of a fluid, neither rismg to the surluce nor sinking to the bottom It may however be proved by experiment that a hollow ball of copper, such as is used for a ball-tap, may be constructed (>f such a weight relatively to its size that when placed in water It will remain where it is placed, just as tlie body A is re presented in the diagram, 59. Ex. II. Find the conditions of equilibrium for a body of uniform density wholly immersed in a fluid and in part supported hy a string. Let a body the measure of whose volume is V be suspended .^a st„,.g fron, t„. fixed point A .0 a, to flo.t bc.owrt' The body is kept at rest by (1) its weight, (2) the pressures of the fluid on its suritxce, \v>j tlie tension of the sti'ing. fi i w BODIES UNDER THE ACTIO N OF FLUIDS. 33 ItDW (1) is equivalent to a single resultant acting vertically doicnwards through the centre of gravity of tho body , (2) is equivalent (by Art. 57) to a sinj^lo resultant, equal to the weight of fluid displaced and acting vertically upwards through tho centre of gravity of the fluid displaced : (and these two centres of gravity coinciding) therefore (3) must act (see Statics, Art. 52) upicards in the ver- tical lino through this common centre of gravity^ and (1) must be equal to the sum of (2) and (3). Hence, if *S' be the nie;isure of the specific gravity of the body, ^' ofthe fluid, ^ of the tension of the string, there is equilibrium when or r= v(s-sr), Ex. A piece of metal, whose specific gravity is 7-3 ano volume 24 cubic inches, is suspended by a string so as to be wholly immersed in water. Find the tension of the string. Taking 1 cubic inch as tho unit of volume, and conscqueJi*^* -„ oz. as the unit of weight, ■I ■\:- m 1000 tension of string =- 24 (7-3 - 1) x ^ oz. 1 /28 24x6;^ X 101 »0 1728 OS, ^8Y5oz. 0.B. 8 34 ON THE CONDITIONS OF EQUILIBRIUM OF 60. Ex. (3) // a body of unif^'^\ i dcnsit>j be immerned in a fluid and he prevented from rising hy a string attached to the bottom of the vessel containhuj the fluids find the tension of the string. \ \i — ../ rl 'i is '■ ti It Hi Let a body, tlie measure of whose volume is V, be kept under the surface of a fluid by a string- fastened to J, a point in the base of the vessel. The body is kept at rest by (1) its \teight, acting vertically downwards, (2) the tension of tiie string, acting vercieally down- wards, (3) the resultant of fluid pressures on the body, acti'f^? vertically upwards. Hence, if T be the measure of the tension of the strinf>-, ^ specific gravity of the body. ^' specific gravity of the fliiidj since there is equilibrium, .'. 7'= ys'- vs BODIES UNDER THE ACTION OF FLUIDS. 35 Gl. To find the resultant presti.ire of a fluid on ii lody partially immersed andfioaling In the fluid. \m Ill- Let ABCD be a body partially immersed and flnatmg iu a fluid, the part BCD being below the surface of thvi tiaid. Imagine the body removed and the vacant space BCD filled with fluid of the same kind as that in wiiich the body floated. Then suppose this substituted fluid to become solid. The pressure at each point of its surface will still be the same as it was at the same point of BCD. The solidified fluid is kept at rest by (1) the attractions exercised by the Earth on every particle of its mass, (2) the pressures exercised by the fluid at the different points of its surface*- Hence the resultants of these two sets of forces must be equal in ma(jnitude and apjyosite in their lines o/actio?i. vacuum.™"'''''""* *'"^ t-'i'-'Ptcr tlie space occupiod by the air is supposed to bu a 3—2 i rij centre of gravity '"'""^ downward, through its through its centr?of glvit!:^ • "" "'^ ™'^'^''"^ "^--'^ as o'LThf;;n::sTe::elhaTt,fir Tr "~ m S""""'" "' '"■'" ""' "»'P'^ "> '"e following example. I' I' •■i J 62. Ex. I. FindthecondUionsofeoidUhrium nf^h ^ floaung and partially immersed iTZrcflr''^'' density. -^^^^ ^f uniform The body ABGD (see diagram in Art. 03) i. kept at rest by o/gr!^ity!'°''' '"™^ ""'"""'^ downwards through centre its Hence (1) weight of the body = weight of fluid displaced ; uispiaiir!:irr/.a,i"'^ •^-"^ "-"^ -' "'^ ^-'^ Tliese are the conditions of equilibrium. i I BODIES UNDER THE ACTION OF FL UIDS. 3 7 63. Ex. II. When a hody of uniforin demify floats in a fluid, the volume of the part immersed is to the volume of the whole body a the specific gravity of the hody is to the specific !j racily of thejc uid. f Let Fhc the measure of the volume of the whole body ABCB V' ' • part immersed BCD, ^ specific gravity of the body, ^' specific gravity of the fluid. Then since, Art. 62, weight of floating body = weight of displaced fluid, '\V' : V :: S '. S\ Ex. A solid, whose specific gravit^y is '4, floats in a fluid vv-hosc specific gravity is 1-2. What part of the solid is below (lie surface? Let X bo the measure of the part immersed m the measure of the whole body. Then co : m=-4: : 1-2; '4 4 1 ii 'Mi i I! f P I. 3^__0JV_77^ CONDITIONS OF EQUILIBRIUM OF 64. The Hydi'osfatic Balance. Jho IT^/drosfatic Balance is a conin.on balance wUli a hook attached to the bottom of one of the scales from wh ch a solid may be suspended and wei.^hed successively (1) in air and (2) when immersed in a fluid. Call the scale to which the hook is attached A and the other scale B Then by the weight of the solid in air we mean tJie weight which when placed in i? balances the solid suspend- ed in air from A. And by the weight of the solid in the fluid we mean the weight which when placed in B balances the solid suspended trom A so as to be immersed in the fluid. The diff'erence between these weights is caused by the pressures of the fluid on the surface of the solid, the resultant ot these pressures being a force acting vertically upwards and eqitimlent to the weight of the fluid displaced hy the solid. Now if Fbe the measure of the volume of the solid, '^ specific gravity of the fluid, measure of weight of fluid displaced by the solid = VS'. Go To compare the specific gramties of a solid and a niiid by means of the Hydrostatic Balance. Let Fbe the measure of the volume of the solid, \ spcLiflc gravity of tiie solid, 5; specific gravity of the fluid. weight of the solid in air. 2 ?/ a] ai /BODIES UNDER THE A C TIOM OF FL UIDS. ,3 Case I. When the solid is of greater specific gravitij than ihefiidd. Let W bo tho measure of tlio weight of the solid in the flui.l, then W- J^' = thc measure of the weight of fliiiil displaced b> the solid, = VS'. Also w^ VS ; ' . VS __ IV "'VS'~ TV-JV" or, '?; = _./Z S' W-W" and thus S and .S" may be compared. Case II. Whan the solid is of less specif c gravity than the fiuid. Attach to the solid sonic heavy substance, called the sinker, which will make the solid sink with it in the fluid. Let w be the measure of the weight of the two bodies in air, ^ in the fluid, y sinker in air, ^ in the fluid Then «?- a? = measure of weight of fluid displaced by the two bodies, y~^= the sinker. Subtracting, ?c-;i;- 2/ + ;? = measure of weight of fluid displacedby the solid = VS'; also W=VS\ • '^-^-1/ + ^ __ S^ " W ~"S' and tlms S and S' may be compared. i !$ « IT?! II . .3 40 o^ -/^:f av^^ov..^^,^,,,^^,,,^ ^^ fie. The eommou IlydromeUr. " Tlio common Hydrometer cniwists ,.f „ , • , terminating in t,vo hollow s„hc 1 r ^ r^"" ''^'"" ^'-^ loaded witl> mercnry, so tliTtt i, V"'' ^- ^^ '» "■""""y fluid with the stem vertL """•""'«»* may float in » Of wl,ieh it ean be t" ," ^t :;' ', ^™r"™^ "^ '"^•™^ the surface of the fluid in wWeh [t fll": '" ™"'°"' '' ''''°" Whose ':;"„: "t^t^" .f ^ ««"• ""- "-«»>•« of bulk of thepart^immlred L r"'' "" ""^ '""''^"™ "^ «"• whol's^ed;: gnX'is!;^^^"' '^ """'^ "'" •»-™- «' bulk of the Par'inn;,l^,H;7''"^'' "'"' "'" ""''^'■^« "' «'^ Ihen weight of hydr„„,oter = ,veight „f fi.t fluid displaced «nd weiMit nf 1 7 ~ '"'"^^ "'® ™'* «f weight ; «cl we.JU of ■Odrometer = ,voigl„ of second fluid disXced - V\ S' times the unit of wei^-ht • '^^^r,^:!^^--^'' »'--and . are 67. Nichohon's Hj/dromeler. 3 II I are An iron stirrup fl«d „ th„ 7 "f \8"PPorti„g a dish O. dish i> A flno wen Ifi 'r«^<""' »f ^ ^Worts a hoavv on the steel wire "'"■'''"^'"' ""k is placed at some point I This instrument is used for two purposes :- ^_^.(1) To compare the specific gravities of a solid and a ea«st\iril;d™uerrsil''' n"1f"/'''^'' P'^^^ ™ <^' the fluid mceL rlel .iZt T" "" "" "" ""'^"'o "^ addr^:rei,t'-^;re':jf;rr^--^ Then measure of weight of solid in air = TV- X, in the fluid= JV^ y .-. measure of weight of fluid displaced by solid = {TV-X)-(^W-Y = Y~Xi . ».G. of solid _ IV -X 8. (jr. of fluid Y—X ' t x t Ih * H\ 13 1 ' '§:,: ii lii It: ii 1 If'* Is 1 43 aV T///^ COMDTTIONS OF EQUriJIUUUAf OF (2) To compare tlic spociHc gravities of two fluif]'^. Let IVXiii the mcaynre of tlio weight of the hytlrometcr, X ami y the mcisurcs of weight to bo placed in C to make the inslrninent sink to B in each iluid. The inoasuro of weigl»t of first fluid displaced - \V+x, sec(/nd = ^^+1/, and, since the volume is the same in both cases, S. 0. of first fluid JV+x S. (r, of second fluid ~ W+y' 68. To compare the specific gramtics of two JJinda by ii'ciffJi lug the same solid in each. Let S and >S" bo the measures of specifie gravities of the fluids, tv> and ?// the measures of weights of the solid when immersed in the respective fluids, W tlic measure of weight of the solid in af". Then IF-wj-meaturo of weight of fluid displaced by solid in one case, )!r-?y'-= measure of weight of fluid displaced by solid [u the other case ; and thus S and S' may be compared. Examples. — IV. (1) A piece of glass when weighed in water loses ^i^ijths of its weight; what is its specific gravity? (2) Find the pressure on 28 miles of a submarine tele- graphic cable whose c'-cumference is .3 inches, the depth of the cable below the surface of tiio sea being 480 feet, and the specific gravity of sea water r026. (3) A body whose specific gravity is 3*3 floats on a fluid whose specific gravity is 4-4 ; what portion of the body will be immersed % (4) If the specific gravity of standard gold be 19"4, and the weight of a .sovereign in air bo 5 dv/ts. 2| grs<, find its weight in water. / BODIES UNDER THE ACTION OF FLUIDS. 43 (5) If a Bubstancc weigh 8 lbs. iu air aiid 6 lbs. in water, what is its specific gravity ] (G) A cylindrical tub of given weight floats witli one fourth of its axis below the surface of a fluid : find the least weight which will totally imnierso the tub. (7) A body whoso specific gi-avity is 1*4 floats in a fluid whose specific gravity is 21; what portion of t'no body is im- mersed ] (8) A leaden bullet, weighing 1 oz., is placed in a glass of water standing on a table ; find the pressure of the bullet on the bottom of the glr-ss, the specific gravity of lead being ir4. C^) A cubic inch of cork floats in water ; find the weight which must be placed upon it to cause the half of it to be im- mersed, the spec; fie gravity oF cork being '24, and the weight of a cubic foot of water 1000 oz. (10) A cork, whose ^\eight is \ oz. and specific gravity '25, is attached by a string to the bottom of a vessel containing water so that the cork is wholly immersed. What is the ten- sion of the string 1 (1 1) A person supports a ball of load, weighing 46 oz. and of specific gravity ITS, wholly immersed in water, by holding the end of a string attached to the ball. What is the tension of the string 1 (12> A vessel containing water is placed in one scale of a balance and weighs 1 lb. A piece of wood of specific gravity •24 and volume 1 inch is attached to the bottom so as to be immersed. What weight will now balance the vessel ? (13) A cube har ging by a string is half immersed in water. If the weight of the cube be a pound, and its specific gravity three tmies that of water, what will be the tension of the string ? (14) A certain substance weighs 30 oz. in water, and 42 oz. out of water. What is its specific gravity ? (15) A substance weighs 14 lbs. in water and 2560 oz. out of water. What is its specific gravity 1 !:f! ti %m 44 ON THE CONDITIONS OF EQUILIBRIUM OF i !i [» ij I ! (16) A substanco wcigliH 12oz. in air : a substauco weigh- ing 20 oz. in water is attacliocl to it, and tlio two together weigh • 18 oz. in water. What is tlio 8i»eciUc gravity of the I'ormer substance ? (17) A picco of mahogany weiglis in air 376 grains, a piece of brass weighing 3so grains in water is attaclied to it, and the two together weigh in water 300 grains. Wliat is the specific gravity of the mahogany \ (18) A piece ( metal weighs 113 grains iu water and 120 grains in air. Wliut is its specific gravity \ (19) A piece of calcareous spar weiglis in air 190 grains and in water 120 grains. Fhid its specific gravity. (20) A body weighs 4 oz. in vacuo, ami if another body which weighs 3 oz. in water be attached to it tlio two together weigh in water 2j^oz. Find the specific gravity of the former body. (21) A piece of wood weighs 12 lbs., and when attached to 22 lbs. of lead and immersed in water the two together weigh 8 lbs. If the specific gravity of lead bo ir35 fintL the specific gravity of the wood. (22) If the sinker be equal in magnitude to the substance wlioso specific gravity is required, but double its weight in vacuo, and if the two together weighed in water would balance the sinker in vacuo, wliat is the specific gravity of the sub- stance ? (23) The specific gravity of cork is -24, and the weight of a cubic foot of water is 1000 oz.; find the pressure necessary to he Id down under water a cubic foot of cork. (24) A cylinder floats vertically in a fluid with S feet of its length above the fluid; find the whole length of the cylinder, the specific gravity of the fluid being three times that of the cylinder. (25) A cylinder floats with \W\ of its bulk above the surface of a fluid whose specific gravity is -820, find the specific gravity of the cylinder. (26) \yiiy is it easier to swim iu salt water than in fresh \ ■ BODIES UNDER THE ACTION OF FLUIDS. 45 (27) Water is ponrcfl into a vcssol containinp; mercury, rtTid tin iron cylimlor allowed to Hinlc tln*ou.jh i\w water floats rtith its axis vertieal in Llio mercury. If the cylinder be I inch in lengtli, lind the lengtli of the portion immonsed in the mer- cury. Tlio spccilic gravity of iron is 7"S, and tliat of mercury i:j-6. (28) A body, whoso specific gravity is M, floats on water; if the weight of the l)ody bo lOOO oz., find the number of cubic inches of it above tlie surface of tlie fluid, (29) A body containing 12 cubic inches weighs in air 8 lbs.; deto';uiino its weight in water. (30) If a cube float on water with one face horizontal, and a body weighing — - oz., when placed upon it, mai;o it sink through an inch, tlnd the size of the cube : a cubic foot of water weighing 1000 oz. (31) What is the specific gravity of a substance, if a hollow rectangular box, ten inches long, eight inches wide, six inches deep, and a quarter of an inch thick, if made of this substance, will just float in water ? (3-2).. A lamina in the form of an equilateral triangle floats . on a fluid with one of its sides liorizontal and its vertex down- wards. If the density of tlio triangle be one-third that of the fluid, lind the depth of it vertex below the surface. (3'Vj , A triangular lamina of uniform tiiickne.^a floats in a vertical position with its base horizontal and its sides half im- mersed iii a fluid : compare the specific gravity of the lamina with that of the fluid. (34) A symmetrical body, weighing 8 lbs,, with a weight on the top floats just immersed in a fluid: how heavy must the weight be, in order that, when it is removed, the box may float with only one-third of it immersed \ (35) Find the specific gravity of a material such that a cylinder formed of it four inches long floats in water with three inches immersed. {^t,'^^ If a cubic foot of water weigh 1000 oz., and a cube whose edge is 18 inc'u?s weigh 2200 oz., how far will a cylinder whose length is 3 inches, formed of the same material as tho cube, sink in water \ i\ :j I i* 46 ON riJE CONDITIONS OF EQUIITBRIUM OF (37) A body, whoso specific fjravity is 2-7 and weight in vacuo y lbs., when immersed in a fluid weighs 2 lbs.; find the specific gravity of the lluid. (38) The specific gravity of mercury is 13*5 and that of aluminium is 2*6 ; how deep will a cubic inch of aluminium sink in a vessel of mercury ? (39) If a body floats on a fluid two-thirds immersed, and it requires a pressure equivalent to 2 lbs. just to immerse it totally, what is the weight of the body 1 (40) If a body weighing 3 lbs. floats on a fluid one-half immersed, what pressure will sink it completely ? (41) A piece of cork (s. g. = "24) containing? 2 cubic feet is kept below water by means of a string fastened to the bottom of a vessel ; find the tension of the ctring. (42) Two bodies whoso weights are Wj and w^ in air, weigh each w in water ; compare their specific gravities. (43) The cavity in a conical rifle bullet is usually filled with a plug of some light wood. If the bullet bo held in the hand beneath the surface of the water, and the plug be then removed, will the ai)parent weiglit of the bullet be increased or diminished ? (44) A body, whose weight in air is 6 lbs., weighs 3 lbs. and 4 lbs. respectively in two diftbrent fluids ; compare the specific gravities of the fluids. (45) A body whoso specific gravity is 7'7 and weight in vacuo 7 lbs., when immersed in a fluid weighs 6 lbs. ; find the specific gravity of the fluid. (4G) A solid sphere floats in a fluid with three-fourths of its bulk above the surface : when another s})here half as largo again is attached to the first by a string, the two S[)heres float at rest below the surface of tlie fluid ; show that the specific gravity of quo sphere is G times greater than that of thu other. BODIES UNDER THE ACTION OF FLUIDS. 47 (47) « A piece of copper (s. g.^-SSo) weighs 887 grains in water, and 910 grains in alcohol ; find the specific gravity of the alcohol. (48) A uniform cylinder, when floating vertically in water, sinks a depth of 4 inches ; to %vhat depth will it sink in alcohol of specific gravity 79 ? (49) « A compound of silver (s. G.= 10-4) and aluminium (s. G. = 2-6) floats half immersed in a vessel of mercury (s. G.= 135). What weight of silver is there in 10 lbs. of the com- pound % (50) An iron rod weighing 10 lbs. is supported b/ means of a string, one-half of the rod being immersed in water. What force is exerted by the string, the specific gravity of iron being 7-8? (.51) A piece of silver weighing 1 oz. in air weighs "905 oz. in water, what is its specific gravity \ (.52) Two bodies weighing in air 1 and 2 lbs. respectively are attached to a string passing over a smooth pulley ; the bodies rest in equilibrium when they are completely immersed in water. If the si^eciijc gravity of the first body be twice that of watc;-, find the specific gravity of the second. (63) A cylinder 9 inches in height, specific gravity ^. floats in water with its axis vertical ; find the height of the surface of the cylinder above the surface of the water. Shew that if each division of the stem of the common (54) 1 hydrometer contains ~th part of tlie bulk of the hydrometer, the ratio of the specific gravities of two fluids, in which the hydronieter floats with x and y divisions of the stem out of the fluid respectively, is equal to m-y \ m-x. (55) To a body which weighs 3 lbs. in air a piece of lead which weighs 5| lbs. in air is attached, and the two together weigh 1;\ lbs. in a fluid whose specific gravity is 4. Find the specific gravity ofthe body, that of lead being 11. - (56) ^ A substance weighs 10 oz. in water and 15 oz. in alco- hol, the specific gravity of which is -7947 times that of water : find the muuber of cubic inches in the substance, taking the weight of a cubic foot of water as 1000 oz. J;, ' I 48 ON THE CONDITIONS OF EQUILIBRIUM OF ^ » (57) A block of ice, tho volume of which is a cubic yard, is observed to float '.vith „^ths of its vohime above tho surface, and a small piece of granite is ; .en embed<^ed in the ice ; find the size of the stone, the specific gravities of ice and gi'anite being respectively '918 and 2'65. (58) A cubical block of wood weighs 12 lbs. ; the same bulk of water weighs 320 oz. ; what part of tho wood will be below the surface when it floats in water ? (59) A board 3 inches thick sinks 2^ inches in water : what will a cubic foot of the same wood weigh, if a cubic foot of water weigii 1000 oz. ? (60) The specific gravity of beech-wood is '85. What por- tion of a cubic foot of that wood will be immersed in sea water whose specific gravity is r03 % (61)j A cubical iceberg is 100 feet above the level of tho sea, its sides being vertical. Given the specific gravity of sea water=r0263 and of ice = -9214, find the dimensions of the iceberg, (62) If a body of weight W float with three quarters of its volume immersed in fluid, what will be the pressure on a hand which just keeps it totally immersed ? (63) > Two hydrometers of the same size and shape float in two difierCnt fluids with equal portions above the surfaces ; and the weight of one hydrometer : that of the other \\m \n\ com- pare the specific gravities of the fluids. ^ (64) A hydrometer, loaded with 40 grains, sinks 4 inches lower when floating in a fluid whose specific gravity is -3 than in water ; without the weight it rises in the water one-twelfth of an inch higher : find the weight of the hydrometer. (65) s If the volume between two successive graduations on the stem of a hydrometer be yoW^i P^rt of its whole bulk, and it floats in distilled water with 20 divisions, and in sea watfcr with 46 divisions, above the surface ; find the specific gravity of sea water. {^%)- A piece of lead is found to weigh 13 lbs. in water, and when a block of wood weighing Gibs, is attached to it the two together weigh 8 lbs. in water. Find the specific gravity of fchn WftnH BODIES UNDER THE ACTION OF FLUIDS. 49 (67) -What is the weight of a hydrometer which sinks as deep in rectified spirits, specific gravity '866, as it sinks in water when loaded with 67 grains ? (68) ^ Tlse weight of a body A in water of specific gravity = 1 is 10 oz., of anolhe/ body B in air whose specific gravity = •0013 is 15 oz.; whUe A and B connected together weigh 11 oz. in walck-: shew tllut the specific gravity of B is 10713. (69) • A substance x^ighs 20 oz. in water and 25 oz. in alco- hol, the specific gvavity of which is '7947 times that of water ; find the number of c\j6ic inches in the substance, taking the weight of a cubic foot (f water as 1000 oz. I ^41 ii ,' I y } a. n fifc CHAFl'ER V. On the Properties of Air. \ t. 69. The thin and transparent fluid which surrounds us od all sides, and which we call the Air or the Atmosphere, is a material body which possesses weight and resists compression. We can prove by experiment that even a small mass of air has an appreciable weight, by exhausting the air from a glass vessel (by a process which we shall describe in the next article). We then find that the vessel weighs less than it weighed before the air was taken out of it. That the air resists compression is evident from the force required to drive down the piston of a syringe when the open end is closed. -'I" >M Every body exposed to the atmosphere is subject to a pressure of nearly \T^ pounds on each square inch of its surface. We feel no inconvenience from this great pressure, because the solid parts of our bodies are furnished with incom- pressible fluids, capable of supporting great pressures, while the hollow parts are filled with air like that which surroimds us. ^ Also, since the atmosphere acts equally on all iiarts of our bodies, we have no difiiculty in moving. \\ ON THE PROPERTIES OF A IK. 5T 70. Hawkslee^s or the common Air Pump. n m ifii IS a AB and DEqxq two pistons with valves opening upwards, which are worked up and down two cylindrical barrels by means of the toothed wheel W in such a way that one piston descends as the other ascends. The barrels com- municate, by means of valves at C and F opening upwards, with a pipe leading into a strong glass vessel V called the receiver. Suppose B to be at its lowest position and therefore E at its highest position. Then as B ascends the valve at B closes, and the air in the receiver and pipe opens C and expands itself in the barrel. As soon as B begins to ascend E begins to descend, the valve at E opens, the valve at F remains closed. The air which before occuijied the receiver and pipe, now occupies the receiver, the pipe, and one of the barrels, and is therefore rarefied. Now let the wheel be turned back : then as E ascends the valve at E closes and F is opened, and meanwhile B is opened as it descends, and C being closed, a quantity of the rarefied air is taken from the receiver and pipe. This process may be continued till the air in the receiver is so rarefied that it cannot lift the valves at C and F, and then tJie action of the instrument must cease. 4—2 s» ON THE PROPERTIES OF AIR, 71. Smeaton^s Air Pump. A ^v :b y D AC is a cylindrical barrel communicating with a strong vesse D called the receiver. At A and C, the ends of the barrel, are valves opening upwards. A piston with a valve B opening upwards works up and down the barrel. Suppose the piston to be in its lowest position. Then as the piston ascends, the pressure of the air being removed from the upper surface of the valve at C the air m DO opens C and expands into the barrel, while' the valve at B is closed by the pressure of the atmosphere. Thcis a quantity of air is drawn away from the receiver As soon as the piston begins to descend, the valve at A is closed, B opens and C is closed, and no external air comes mto the barrel or receiver. When the piston again ascends the air in the barrel i*- ag^ drawn out. ON THE PROPERTIES OF AIR. 53 The only limit to the exhaustion of the air by this pump arises from the difficulty in making the piston come into close contact with the valves at A and G, Note. The advantage of Smeaton's Air Pump is that since the valve at A closes as soon as the piston begins to descend it relieves B from the pressure of the atmosphere, and the valve at B is opened by a very slight pressure from the air beneath. Hence this pump is capable of producing a greater degree of exhaustion than Havvksbee's. ».1 72. To find the density ^of the air in the receiver of Smeaton's Air Pump after n ascents of the piston. Let the measures of the capacities of the receiver and the barrel be respectively x and y. Then the air which occupied the space whose measure is x when the piston was at C, will occupy the space whose measure \%x-vy when the piston comes to A^ , density after one ascent _ x density at first •I A.' ^• + 2/ X :. density after one ascent = ^^^. (density at first). Similarly, x density after second ascent = . (density after one ascent) and so on ; .*. density after wth ascent = f j (density at first). The same formula is applicable to Hawksbee's Air Pump, if a? represent the measure of the capacity of the receiver and pipe, and y the iiicasurc of the capacity of eacli of tho barrels. m \ *v%-\ M ^^ 54 ^TJIE PROPERTIES OF AIR, 73. The Barometer. i ii of S~u " " '*"™"* '""• """'™""^ '"o P~ end .4, invertli.etah! "t with mercury : if wo then close the surfaceofthemercnrinf, ? •'«'-';'»7 ". the tube from the e oi tne niercuiy m the basin, is from 28 to 31 inches atniltett'm'^"rshf™ r"";"^'^" '''■ "'" P— "' 'ho the receiver ofan air nr,m' t""^ 'l'.' "'^'™""^"' ""-^^r ON THE PROPERTIES OF AIR. 55 74. To shew that the j)i^*issure of the atmosphere is ac- curately rejyresented by the weight oftJie column qf' mercury in the Barometer. Take in the surface of the mercury in the basin an area M equal to the area of the horizontal section of the tube at D. Then area J/=area of the base of the column of mercury in the tube, and since tliese areas are equal and in the same horizontal plane, the pressures on them are equal. Now pressuvn downwards on J/ — atmospheric pressure on area M, and i/ressure downwards at Z) = weight of column of mercury CD. Therefore the atmospheric pressure on area M is equal to the weight of the column of mercury CD. It follows then that the atmospheric pressure on any area is equal to the weiyht of the column of mercury in the barometer, having the same area for its base. Consequently the weight of the column of mercury in the barometer is tlie proper representative of the pressure of ths atmosphere on a given surface. tvl 1 .p. % n t' f s« OAT THE PROPERTIES OF AIR. 7.1. TT(Mico it fulIowH tl.Mt tho height of the column <if niercmy in tlio biironaitor jh pro- i portioiml to tho prossuro oC tho atmo- sphere. Tf then wo liiivo a vortical tubo of uni- form boro lillcd up to tho level D with mercury, if I) bo exposed to tho atmo- splierie proHHuro and if M bo some other level in tho tubo, and if A bo tho hei-ht of the barometric column, D - U ^^- - — prossuro nt /> ^ jvei^j»Uf^c(ju^^ mercury of hri-rht h pressure at M we;-ht of a col. ofiiiercu:7«)fheightl/r+^7>J^ h h + DM' 76. To find the A tmospheric Pressure on a Square Inch. ^ Tho pressure of tho atmosphere on a square inch is dotcr- nnned by frnding tho wei-ht of a column of mercury ^^■\u,Ro base IS a square inch and whose height is the samo as the height of tho colunm of mercury in the barometer. Taking the specific gravity of mercury as 136, the weight of a cubic foot of distille<l water as lOOOoz, and the height of the barometric column at tli. level of the sea as :50 inches, we have pressure of atmosphere on a square inch - (^30 X 1 X 1 X —^ X 13-6 j ounces, _30x 1000x1.36 1728 xTd '^''"^^«' • 236^- ounces, = 14ifif lbs. OlSr THE PROPERTIES OF AIR. 57 77. In catimiitini? tlio pressnro at a point in tlio interior of fluid ('xp()H(!(l to the alinoHplicric proHsuro, wo must add to the p»'essuro on a unit of area contaiiiinj^ tho point tlio tttmospheric prcssuro on a unit of area. Supposo for iuHtatico wo have to find tho i)rcHsuro at a depth of 100 I'eet in a lake, f 1) neglecting atnjospheric pressure, (2) taking tho atmoHpharic proHHuro into account. Take a Sijuaro inch aa tho unit of area : then (1) I'resaure at depth of 100 feet on a square inch = weight of a column of 'ivater 100 feet in height, resting on a haso of a square inch = weight of a column of water whoso cubic content is (100 x 12 x 1 x 1) cubic inche^j /I 200 ,, A (^^^^xlOOOJoz. lbs. _ 1200x1000 1728x16' = 43^ lbs. (2) Pressure at depth of 100 foot on a square inch / 29 \ = f 43 2 + 15] lbs. nearly, 2f) = 58 r^ lbs. nearly. 78. The Atmosphere is most dense at the surface of the Earth, and its density diminishes with its height. Hence as one ascends a mountain tlio weight of tho incumbent air is diminished, and tho mercury in tho barometer sinks. Thus the barometer furnishes a means of ascertaining approximately tho height of a mountain. 7J). a Barometer might be formed with any fluid, but mercury is preferred to other fluids because of its great density. A Water-barometer must have a tube of great length, since the atmosphere supports a column of water m oro than 13 times as high as tho colunm of mercury supported in th(3 uiorcurial barometer. .^. w Hi »» ' 58 ON THE PRO PERT IKS OF AIR. 80. The pressure (if a given quantity of air, at a aiten temperature, varies inmrsely as the space it occupies. Tlio following proof by experiment ostablisLes the truth of tills law. I ^f ^.'n"". ^'''°*^ *^^''' cylindrical, uniforn. and vertical. The branch AB is much longer than the branch BC. The ends uro open. "^ Mercury 18 poured drop by drop into the end A till the Humice o thc^mercury in the two branches stands at e same level at P and Q. The end C is then closed. The« the pressure of air in C(2= the atmospheric pressure. Let mercury be again poured in at A, (the effect of which 8 to compress the air in CQ,) till the surface of the mercury in the shorter branch stands at li, halfway between (7 and Q. u-ni^V'i^T ^""''^^ *^'^* *^^ "^^^"^^^y "^ <^ho longer branch r^.ZfnMrMl ""' T""'''^' ''''' '^''^''^ '' thf column of height of the barometer at the time of making the experiment ON Tim PROPERTIES OF AIR. 59 Now pressuro at M- prcssuro at 7?. till the at the But proMsure at J/= weight of cohiinn of mercury DM 4-pro.ssuro of iitmosphcrc ut />, = atmospheric prcssuro + iitmospherio IM-essure = twieo tho atmospheric pressure ; .'. pressure of tho air in CR = twice tho atmospheric pressure. Hence tho pressure of tho air in CR is twice as gi-eat as was tho pressure of the air in VQ. That is, when tho given quantity of air in CQ has been compressed into hal/i\\Q space, tiie pressure of tho compressed air is twice as great as it was at first. 81. Tho proof given in tho preceding Article may bo put in a more general form, R being any point between (7 and Q, thus : — Let mercury bo again poured in at A till tho surface of tho mercury stands at D and R in the branches, and let M be level with R. Then it is found that if tho spaces CQ, CR successively occupied by tho air bo measured, and if h bo tho height of tho barometer at the time of performing the experiment, ^m space CQ, _h + DM space OR ~ h Now it is clear by Art. 75, pressure supporting air in CQ h pressure supporting air in CR h + DM* .N • pregs ufo of air in CQ _ CR pressure of air in CR ~ CQ' lii 6o ;■ S ON THE PROPERTIES OF AIR. Cor. Flenco r/o can shew that the elastic force of air varies as its density. For since the same quantity of air is confined in CQ and CR ^ density of air in CR : density of air in CQ, :: Cq : CR :: pressure of air in CR : pressure of air 'mcq. 82. The Condenstir. (f B ^* 'I »» ■» ^C is a cylindrical barrel with a valve at the bottom, G, opening downwards into a vessel B, called the receiver. A piston with a valve A, opening downwards, works in the barrel. Suppose the piston to be at the top of the barrel. When the piston descends, the air in the barrel being condensed closes the valve at A, and opens the valve at C. Thus the air which was contained in the barrel is forced into the receiver. When the piston is raised again, the denser air in B keeps the valve at C closed, while the pressure of the atmosphere opens A, and the barrel is refilled with at- mospheric air, wliich is forced into the receiver at tiie next descent of the piston. The process may be continued till the required quantity or air lias been forced into B. * -i j b P r r( ti tt rce of air ed in CQ sure of air ON THE PROPERTIES OF AIR. ftr 83. To find the density of the air after n descents of the j)iston. Let X and y be the measures of capacities of the receiver and barrel respectively. Then the air which occupied the space whoso measure is ic + y, when the piston was at the top of the barrel, will occupy the space whoso measure is x when the piston comes to the bottom of the barrel ; .• density of air in receiver^a^ter onedcscent cc + y density of air at first "^ ~ ~^ ' .-. density of air after one descent = "^-"^ •' . (density of air at first). Similarly, density after second descent- ~-^ . (density of air at first) and so on ; • •/ density after nth descent = ^,^ . (density of air at first). I' ii L I I )ttom, (7, ;iver. A J in the When •ndcnsed -'hus the into the er air in of the vith at- iie next iuantity Examples.— V. (1) If the capacity of the receiver in Smeaton's Air Pump be ten times that of the barrel, what will be the exhaustion produced by six strokes of the piston ? (2) Find the pressure of the air in the receiver of an Air ■ Pump after two strokes of the piston, the volume of the receiver being eight times t];at of the barrel. (3) Find the ratio of the volume of the receiver to that of the barrel in the Air Pump, if at the end of the third stroke trie density of the air in the receiver : tlie original density :: 729 : 1000. •I' \ » iJ i ■) 62 ft- i I ll OAT THE PROPERTIES OF AIR. (4) Is it necessary tlnit the section of tlic tube through wlucli tl.omereiir.yn.es in the barometer should be t]ie same tnroughout ? (o) Assuming that a cubic foot of water wcijrhs 1000 02 and a cubic nich of mercury weighs 1% oz, find tlie pressure on a square inch at a depth of .90 feet below the surface of the sea, when the barometer stands at 30 inches. in f^' \?''f y ^^•'' ''''*'^" '''^ ^''^^ '^^''^^" '''^^ barometer bo 10 times that o a section of tlic tube, and the mercury fall 1^ inches in the txxh^,, Hnd the true variation in the height of the mercury, and draw a figure reivfesenting the instrument. ?i 1 ^\^ ^''^^ '''"''' '"^'^^ ^" *^'^ ^"^^ of •'^ barometer, what would be the effect ? , rtt (8) If the weight of the column of mercury which is above the exposed surfiice in a barometer be an ounce, and the area of the transverse section of the tube ^ of a square inch, what is the pressure of the atmospliero on a square inch? (9) When the mercurial barotneter stands at 30 inches what wdlbe the height of the column in a barometer filled with a fluid of specific gravity 3-4, the specific gravity of mer- cury being 13-6? T..^T,^ ^^'■^^"^^^^^' ^^i" it have any effect on the indica- tion of the instrument? (11) If a body were floating on a fluid, with which the air' was m contact, and the air were suddenly removed, would tlip body rise or sink in the fluid ? ' ^ (12) What would be the eflfect of admitting a little air into the upper part of the tube of the Barometer ? (13) A pipe carries rain water from the top of a house to a aigc tank, the surplus water in which escapes throuoj, a valve in the top which rises freely. A weight of 21 lb is placed on it and it is found that tiie water rises in the pipe to tlie height of 20 feet before the val r.pons. Find its area assuming that the height of the Water- Barometer is 34 feet' Rnd the atmospheric pressure 15 lbs. on the square inch. /. IR. tube through ' be tJie same ?ighs 1000 02. the pressure mrface of tlie •urometer bo 3rcurv fall \\ loight of the umeiit. meter, what rich is above md the area e inch, what I? ' 30 inches, neter filled 'ity of nier- ontained in the indica- lich the air" would the 1 little air a house to througli a ■ 21 lbs is n the pipe id its area, is 34 feet iich. ON THE PROPERTIL:, OF AiK. ^l (14) -A cylinder filled with atnios])]icric air, and closed by an air-tiglit piston, is sunk to the depth of 500 fathoms in the sea; required the compression of the air, assuming the specific gravity cf sea- water to be ro27, tiie specific gravity of mercury 13"57j and the height of tiio barometer ;50 inches. 05) A barometer is sunk to the deptli of 20 feet in a Like: find the consequent rise in the mercurial column, the specific gravity of mercury being 13 '5 7. (16) If a body, exposed to the pressure of the air, float in water, prove that it will rise very slightly out of the water as the barometer rises, and sink a little deeper as the barometer fiills. (17) V Water floats on mercury to the depth of 17 feet, compare the atmospheric pressure with the pressure at a point 15 inclics below the r-irface of the mercury, takhig into ac- count the atmospheric pressure on the surface of the water, having given that the heights of the mercurial and water barometers are 30 inches and 34 feet i-espectively. (18) Explain clearly why a balloon ascends. (19) Explain how it is that a bladder filled with air, will, if conveyed deep enough in the sea, sink to the bottom. (20) What would be the height of the column of mercury (s. G.= ].T5G) corresponding to a pressure of 14 lbs. 2 oz. on the square inch \ (21) .A cubical vessel full of air, whoso edge equals n inches, is closed by a weightless piston. Find the number of pounds which must be pl;ced on the piston in order that it may rest in equilibrium at a distance of 2 inches from tlie bottom of the vessel : the [ircssurc of tiie atmosphere being 15 lbs. on a square inch. (22) -The lower valve of a pump is 30 feet 4 inches above the surface of the wat- r to be raised : lind the height of the barouioter wlien the pump ceases to work, the specilic gravity of mercury being 13'6. ,i»'! ■^ 64 ON THE PROPERTIES OF AIR. (23) It IS found that the cork of a bottle is just driven out when the pressure .f tiio air svithin is double that without • tho bottle IS then filled with mercury i.nd inverted, and it is a'-ain iound that tlie cork is just driven out. Given that °the barometer was standing at 30 inches at the time, find the height of the bottle. I I * r i 1 . ^^'^ ''^*^''' ^^ *^'^ ^'o^^^'"e Of the receiver to that of the barrel m a Condenser, if at the end of the tliird stroke the density of the air in the receiver : its original density ^ (25) A hollow cylinder closed at tho upper end and open at the lower is depressed from the atmosphere into water, its axis being kept vertical, and is found to float with its upper end in the surface of the water. Wluat will be the effect on tlie cylinder of an increase of atmospheric pressure ? cJ'^^l ^^ ^'"^ ''""^''"''^ ^^ *^'® cylinder in a Condenser be one- fifth tne vo ume of the receiver, find the pressure at any point oi the latter after 20 strokes. ' (27) The pressure at the bottom of a well is double that at Che depth of a foot; what is the depth of the well if the pressure of the atmosphere be equivalent to 30 feet of water ? (28) A cubic foot of water weighs 1000 oz. ; what will be the pressure on each souare inch of the base of a cube whose edges are 10 inches, when filled with water ? 1 '< (29) A cubic foot of water weighs 1000 ounces, and the pressure of the air on a square inch is 236 omices ; find the pressure on 16 square inches at a depth of 9 feet below tho suriace of a pond. (30)' If4^, C, be three points in a uniform fluid at rc^t the three points being in the same vertical line, and tho dif- ference of the pressures at A and ^: difterence of the pres- sures at A and C as ;> : q, find the ratio of AB to BG. (31) Explain the princ'ii)!e of the Air-gun. ON JN/i PROPFRTIT'S ( ^ AIR. driven out :.Iaout ; tho it is again that the , find tlie 3r to tliat rd stroke ! density and open -vater, its its npper effect on be one- at any ible that il if the water ? 65 < (32)« If tho area of tlie basin of a barometer be 17 times that of a section of the tube, how ought tlie si cm to bo -gradu- ated in order that the reading may give the true height of the barometer ? (33) If the specific gravity of mercury be 13*57, and the weight of a cubic inch of water 252G grains, find tlie pressuro of the air on a square incli in lbs., when the mercury in the barometer stands at 30'5 inches. • (34) . If the tube of a barometen be 36 inches long, and, on account of air being in the upper part, the instrument stands at 27 inches, when a correct instrument stands at 30 inches, what length of tube would the air fill when reduced to atmo- spheric density ? (35) The specific gravity ot the weights employed by jewellers, for weighing i)reci()us stones, is greater th .11 that of the stones themselves. Is it more advantageous for the jeweller to sell stones when the barometer is high, or when it is low ? (36) f A tube closed at both ends and 2S inches long is half filled with mercury, the remaining portion being occupied with air at atmospheric pressure. If the tube be placed in a verti- cal position with the mercury uppermost, and the upper end be opened, find how fiir the mercury will sink, the height of tho barometer at the time bein^ 28 inches. :i t will be e whose % i and the find the ;low tho at rc^t, tho dif- prea- i Nil &H. J* 1 1 ' CHAn'ER VI. On the Application oj /ifr. ^\ Tlie Diving Bell. i\ ' I ,0^ >■*■■ >• if i 4 .IJ If a glass be inverted, and witli its month horizontal be pressed down into a basin of water, it will be seen that though some portion of water ascends into the glass, the greater part of the glass is without w^'^tcr. This is caused by the Cdmpressionof the air, which prevents the water from rising in tlie glass. The Diving Bell works on the same principle. A heavy iron chest BCED, open at DE, is suspended from a rope A, and lowered into the water, with its open end downwards. The water will then rise till the air in the chest is sufficiently compressed to prevent the water from rising beyond a certain height MN. Air is pumped in occasitmally through a pi] to /', and the impure air is allowed to escape through :uiother piv- ' Q. ■"'^-*. ON THE APPLICATION OF AIR. 67 >sft. The Common or Suction Pump. 1-* I) I Al ABh'A cylindrical barrel in which a piston P, withavalvo opening upwards, is worked up and down by the handle R. ItCiH a pipe, conimunioating with the barrel by u valve, oi)en- ing upwards. The end C, which is pierced with ii number of small holes, is placed under the surface of the water which is to be raised. Suppose the piston to be at the bottom of tlie barrel. Then when the piston is raised the valve P is closed by the pressure of the iiir on its upper surface, r.iid tlici-e being little or no air in PB, the valve B is opened by the action of the air in BC, and as it continues open during tJie whole as- cent of the piston, the air in BIl, the part of the suctitm-pipe above the surface of the water, expands into the barrel, and becomes less dense than the air which presses on the water v>utsido the sucti()ii-[)ipe. The water is consequently forced up the pipe by the i)ressurc of tiie atmosphere, till the pressure downwards at 1/ is equal to the atmos|)lieric pressure. When the piston descends the valve B closes, and the air m PB, being condensed, opens the valve P. This process being continued, the water will at length rise through the valve B, and at the next ascent of the piston a mass of wat'T v'U be lifted and discharged tlu'ough the sp^'Ut D. •t 1 6S 0!f Tim AITUCATION OF AIR. 0. '^l^t^^T" "i" '■■" "-^"ci«i.tofacoi;;;;;; 86. TJie Forcing Pump. 1^1 '• . -o .-\L' ^^ is a cylindriuil barrel in whic. u solid piston P ia worked up and down the space AF. BGh a suction-pipe of whtcli the end is placed under the surface of the water. BE is a [)ipe communicating with the bairel. At B and Z> arc valves opening upwards. Suppose the piston to be at the bottom of its range in the barrel. Then when the piston is raised the valve at D remains ON THE AITUCATION OF AIR. 69 closed, tho air in Z>/?/^ expands as the piston rises, and tlio air in BII opens tlic valve B and expands into tho barrel. Tho water is tliercfoi'O forced up tlio suction-pipe by the pressui'e of tlio atmosphere. When tho piston descends the air in PFBD is condensed, closes the valve B, opens tho valve i>, and escapes through Z>. When the piston ascends again the water rises higher in BG, and this process is continued till tho water rises through B. Thou tho piston on its descent forces tho water up the pipe DE. •«') 87. In order to produce a continuous stream through the pipe at E, the pipe is Introduced into an air-tight vessel Dll into which the valve D opens. JE / ^ I •^v^i^i--^^^. etI"---^ -~-o. z =£^!yizf D r*" — re« " " u^ — 1 - 1 i v- — 1 1 -A en -'11 J When the water has been forced into this vessel till it rises above 0, the lower end of the pipe, the air which lies between the surface of the water in the vessel and the top of tiie vessel is suddenly condensed at each stroke of the piston, and by its reaction on the water forces it through the pipe OE in a con- tinuous stream. wf 70 I I !l I 'i 'H 8S. T/w riro Enfjlue. Tliis macliino consists of a donl,l„ t ■ r«.«ps co„„„„,.icati„g ,vith thesatatvcre'ri;''"'"''' """" T1.0 pipe r dcccnd. into a .■c.,,e,-voh. of n-atcr ' n.o valves opening „p,vards are at F, F- ,, ,, ^ ^ ^^..s a fixed beau, round ,v,,iol. the pi.,tu,-rods Jork ' '"- ''""■•'' '" '''=«''« '■S'^d llirougi, the pipe //. ON THE APPfJCATIOiV OF AIR. 7< S.'». The LijVmg Pump. ^r H W: AB is a cylindrical barrel in which a piston with a valve J/ openin<^ upwards works, the piston rod passing through an air- tight collar at A. BO is the suction-pipe of which the end G is placed under the surface of the water. DE is a [)ipo up which the water is to be raised. At D and B arc valves o[)ening upwards. The water will be brought within reach of the piston by a process similiir to that which has been described in the case of the other piuups. When le piston nscends lifting water the valve at Z) opens, and the water is discharged into the pipe DE. When the piston descends, the valve at D closes, and prevents the return of tlio water in DE into the barrel. ». Each stroke of the piston increases the quantity of water in DE, and thus the water may be niiscd to any hciglit, provided that the barrel AB, the pipe ED, and the piston rod be strong enough to bear the pressure of the superincunibout column of rrater. m u t ; ^ .. t 7a ^^ Tim APPLICATION OF AIR. 90. The Siphon. »ipi,ri:; y;,"!!!'' -^ '"» "-•'« ^-f^- -.. th., .ra„e,.„: of ti,o P»i"t of the ».>ho,iltf,i' rr''""' 1'"" ^' "'0 '"Shest of the fluid : thei " "^*''" "'''''°"' "' "'o ™rface pressure of atmosphere at //i„ dircctio,. ^5 = pres,„re on area Z), pressure of atmosphere at ^'in direetion (7Z? = pre,.„re on area Z>, ••• pressure of atasphere at //i„ direction /«=press«re of atmo«phcro at C in direction CB 4rof''c'ir of«:inrLi/ ■' *'r'^"<"' "^ "•« o^. dimi,,.,hea h. the weif^f-ro/r rfl:[;Sar ON THE APPJJCATJOh' OF A IP, 73 fcho column liC h proator than (-(.liunn /?//; tlio cfTectlvi', pro; 8uro of ittniosphoru in direcl.ioii /// prossuro of atnio.spliero in di will bo driven by tho elYuutivu atnio.-^plicric prcsHuro iu a cou tinuous streuui iu tho Uirootiuu UBC. 'j is <,^rtMter tlian i\w ell eel Ice I 91. On intennitling ^j^rings. rnteruiitting Springs arc springs which run for a time, then Ptop for a tinio, aud then begin to ruu again. This phenomenon is explained by tho priuciplo of tho Siphon. Lot A bo a reservoir in a hill in which water is gradually collected through fissures, as B, C, Z>, communicating with tho external air. A Now suppose a channel MNR to run from A, first ascend- ing to N and then descending to R, a place lower than tho reservoir. As the water collects in A it gradually rises in the channel to iV, and then flows along NR, and by the principle of the Siphon it will continue to H'vv till A is completely drained. Then the flow ceases till the water in A has collected suflicient- ly to reach N. ■4^ f . t ■ \ 7^ OJV THE APPLICA TION OF AIR. 92. Bramah's Press. Tho^ Hydrostatic Press, generally called Braniah's Press, is a machine by which an enormous pressure is obtained by means of water, tiie only assicrnabio limits to its power being the strength of the materials of which it is formed. ^ ^ C is a forcing-pump, by the action of which water is forced mto a tube BD, which has a valve B opening inwards. ^ is a strong cylindrical piston, with a base many times larger than t!ie base of the piston A, working in a vvater-ti«-ht collar at M, N. " 111 P Between the top of the piston E and a fixed beam FG, a bale of goods, such as paper, cotton or wool, is placed. Suppose the area of the base of E to bo 200 times that of the base of ^. Then if a pressure of 100 lbs. be applied to A, a pressure of (200 X 100) lbs. or 20,000 lbs. will be conveyed to the base of E. ihus any amount of pressure may be applied fo JV, eHlier by mcreasing the pressure applied to A, or by making the base Qt ^ larger m comparison vvitl) the base of A. UN THE APPLICATION OF AIR. 75 s Press, is by means the being r is forced s. my times ater-tig!)t nFG,a. 3 that of (ssure of so of E. ^, either the base Examples. — VI. (1) What will be the clfcct of making a small aperture in the barrel of a Forcing Pump ? If the piston work uniformly up and down the length of the barrel, and a small aperture be made one- third of tiic way up the burrel, how much more time than before will bo consumed in filling a tank i (2) If t!io upward motion of the piston of a Common Pump be stopped, when the water has risen to the height of 16 feet in the supply pipe, but has not yet reached the piston, find the tension of the piston-rod, the area of the piston being 4 square inches, and the atmospheric pressure 15 lbs. on the square inch. (3) What would be the efifect of opening a small hole at any {Mjint in the Siphon, first above, secondly below the surface of the fluid in the vessel ? (4) What is the greatest height above the surface of a spring over which its water may be carried by means of a siphon-tube, when the barometer stands at 29 inches, the Bpocific gravity of mercury being 1;JT)7 ? (5) What would take place in a siphon at work if the pressure of the atmosphere were removed 1 (G) ^Vill the siphon act better at the top or the bottom of a mountain ? (7) Could a siphon be emploj'ed to pump water out of the hold of a sliip floating in a harbour I (8) What is the gr(;atest height over which water can be carried by means of a siphon when the mercurial barometer stands at 30 inches ? (9) If the ends of a siphon were immersed in two fluids of the same kind and the air were removed, describe what would take place. (10) A ii'jUow tube is introduced into the bottom of a cylindrical vessel through un air-tight collar ; and a large tube, of v/hich the top is closed, su-peuded over it, so as not quite to touch the bottom : consider the effect of gradually pouring water into the cylinder, until it reaches the level of the top of tl)0 iiivertod tube. :-<i ' ' 4 • m ill ^ t > ii •I - 76 OJV THE APPLICATION OF A JR. (11) A siphon i,s placed with one end in a vessel full of water, and the other in a similar empty one, both of which are on the plate of an air-pump. As soon as the water has cover- ed the lower end of the siphon, a receiver is put on, and the air rapidly exhausted, and then gradually readmitted : describe the effects produced. (12) A siphon, filled with water, has its ends inserted in vessels filled with water ; state what will take place when the vertical distances of the highest point of tlie siphon above the surface of the fluid are both less, both greater, and one greater and the other loss than the height of the Water-Barometer. (13) What is the length of the smallest siphon that cas empty a vessel 2 feet deep 1 *« f . i ssel full of which aro has covcr- 11, and tho : describe nserted in when the abovo the nc greater )mcter. 1 that cas CHAPTER VII, On the Therinometet, 93. The general consequence of imparting heat to bodies is the expansion of their volume. The particles which compose a solid body, as for instance a block of lead, are hold together by tho force of cohesion. It requires a force of great magnitude to increase or to decrease the volume of a block of lead, though lead is a soft metal. The ai)plication of iieat, by we ikening the force of cohesion, reduces lead and other metals to a liquid state, pushes the particles more widely apart, and thus increases the volume of the bodies to which it is applied. If heat be applied to a liquid, as water, the cohesion of the particles is weakened, and they nltimately acquire a tendency to break away from each other and assume the form of a vapour. If heat be applied to an elastic fluid, as air, it causes it to expand. Thus if a bladder, partly full of air, be placeil before a fire, the air will expand and distend the bladder. Again, if a piston P exactly fits a cylindrical tube AB, and is supported by the condensed air ia PB, if heat bo ai)i)lied to the air in PB it will expand and raise tho piston. 78 ON THE THERMOMETER. .♦i 1 '»\ .ft I closed ".T'^'f f;"'"''.™ '"'" "f ""''■<"■"> •«»-° ha b ,lh 'ri'"'; ''•''■"""■■""'S at «'<•■ other end 0.1 nu'f ,,''"''"""'""*'"'» "'"■•oury, whicl, ex- betwci; M,„ '™^ ",'' ""-' "•''^■- ■J'l"> »I«ce vaaram "■""''^ """^ "'« '"l* "f""' ""'« «a If Oic mercury i„ the iiistrmiuuit bo subiectod tnhfhT'^M "' ""''^'"""^ "^ the upper part of the tube before the end A is closed by n akipc. the 95. 7>) j7m^?^Yri^ « Thermometer. descends and fin.ilv becmn',. «? * '^ ""™'''^' "'« «'''"™ it rests is .narkod t r tl,f ;''""-^- '^'"■' P""" -^^ ''I™'' momoter. "'^ '''■'''■*"''' P"'"'- "f the ther- in. nl::i;;t~^,:-<^:- ™ the :r ^ -^ ™- ^o"- the cohiMin rises and fino v 1 J tlie mercury expands, wi.ich it rests iT, aH.ed ^ ^Zt 7 '""'^- ^'^^ ^^"^^ '^ mometer. ' ''^'' ^'"''^'^'^ ^^^^^^ of the tlier- The space between thr free^inf^ nninf o,. i n u •,• is divided into cq,ud spaces, 0.11:;°^" "'"= """" and'b„S;n;;7i",fe,Iir™'''"'''''^f'-^---^'"S ""-t is n>arkcd 32« boili;;» "oo! ''"''™'^'»«"^-- freezing pointis .uarkcd 0« and 114 ! 8 96. Haol tig gi':cn the viavhcr of degrei TJiermometer^ to p,d the coZZ ;^"^'''"" ^^ -P^hrerheif. ontheCentia^ad/^hJZ:::::^'''^'''^ ''^''^^'^ of degrees liiennoineter. lunent con- i extent of ON THE THERMOMETER. 7V Let AM be the line at which the mercury stands at freezing point, BN at boiling point. 100 ■ JB N d -212 -2P' -32^ m i leaves a lorcury is e column at which the thei-- iter boil- cxptinds, 3 point at ho tlier- ing- point marked "ked 32"^ d 0" and degrees Then AM and BN are marked 0" and 100" on the Centigrade scale 32*^ and 212" Fahrenheit Let the mercury stand at the line PQ^ and suppose the graduations on the sl Jes ^^ be C^ and F'^ respectively. .- AP MQ ^''''ab^mn^ or C F- 32 100 2J2-32' C_ _i^-32 *^^106~ 180 ' C_i^-32 •*• 5 " 9 ' and from this equation we can find G when F is given and /' when C is given. 97. To compare the scales of the Centigrade and Reau- mur's Thermometer, we proceed hi the same way, putting ^0" R, W instead of 32", i^, 212*^ respectively, and we obtain G _R 100 ~ bO ' G R or - = - . o 4 Hence the three scales are thus connected, C F- 32 R 5 9 8o ON THE THERMOMETER. f) V li; Pifi IfL , li.M* 1 ii^ i 111 \ [lli If' 98. The following examples will sliowl^ow to findTtlu. number of de^^reos marked on any one of the three eales tl n the number marked on one of tiie other scales is given Since ^=^32 5 9 ' andi^=5fj, C_ 56-32 5 9 ~ ' .'. 9C=5x24, .'. the reading on the Centigrade scale is 13^ degrees. to ^^^^r^"^ ''' Fahrenheit scale correspond. bince C= 14, 14 ^ i>'-32 5'~ 9 ' .M26 = 5/'^-160, .-. 52'"= 28G, that is, the reading on the Fahrenheit scale is 57 1". E:?. (3) If the sum of the readings on a Centigrade anu a Reaumur be 90, what is the reading on each ? and'^'*' '''' ^'^""^ *''''' equations, from which we can fina ( C H 5=4 (1^' (7+72 = 90 (2); .-. 4C=5i2 I 4(7+ 4/2 =.360 J ' .-. 4/.» = 360--5iif, '. 9i2 = 360, andsoi2 = 40aiid o'=50. Ill I P ON THE THERMOMETER. 81 find tilt! :iles when sn. !e cor TU- 3es. esponds ! anil ii find ( Examples.— VII. (1) Givo tliG number of dcgi-ees in tlio Centigrade and Reaumur's scale respectively that correspond to the following readings on Fahrenheit's scale, (1) 30", (2) 45«, (3) 56% (4) 0«, (5) -7", (6) -45°. (2) Give the number of degrees in the Centigrade and Fahrenheit's scale respectively that correspond to the following readings on Reaumur's scale, (1) 50, (2) 20'>, (3) 0", (4) -18«, (5) -64% (6) 120% (3) Give the number of degrees in Fahrenheit's and Reaumur's scales respectively that correspond to the following readings on the Centigrade scale, (1) 16% (2) 45% (3) 110% (4) 0% (5) -15% (6) -24«. (4) Is it necessary that the section of the tube through which the mercury rises in the Thermometer should be the same throughout ? (5) If the sum of the readings on a Centigrade and Fahren- heit be 60, Avhat is the reading on each ? (G) At what temperature will the degrees on Fahrenheit bo five times as great as the corresponding degrees on the Centigrade ? (7) At what point do Fahrenheit on. ' the Centigi'ade mark the same number of degrees ? (8) Show how to graduate a Thermometer on whose scale 20° shall denote the freezhig pohit, and whose 80th degree shall indicate the same temperature as SO" Fahrenheit. (9) What will bo the reading on the Centigrade when Fahrenheit stands at 78" I (10) The sum of the number of degrees indicating the same temperature on the '^^witigrado and Fahrenheit is 88, find the number of degrees oi« each. (11) What readin,? on the Centigrade corresponds to 49» Fahreiibcit 1 p. n. ® i!^ •I i'.i; •ii ill m m 8. i! ,U. M '» I % (9/V yy/A' THERMOMETER, o limes as fcrut as the corresponding degrees Centigrade ! 10»^-' ™.U,»r ™'™""<'''"- ''""-ks t»o temperatures by9«a,Kl ^o»rLtLT';^;:irt'•^'t^!::?l::"';r^ mark when the former marks le"? ' "'" """""'"• c.-ease h, a given" tlmL'eVo d^ ^ 'find ho': mT", "'■ the tliormometers has risen. ' ' """'' <""='' «' \' \' CHAPTER Vin. Miscellaneous Examples. 99. We shall now give a series of examples to illustrate more fully the principles explained in the preceding Chapters. The important law of pressure in the case of compressed air, of which v:e treated in Arts. 80, 81, will be referred to as MarrioU&'s Law *. Examples worked out. 1. Water is 770 thnes as lieavy as air. At what depth I in a lake 'tcould a bubble of air be compressed to the density ' of 2oater, supposing Marriotte's law to hold good throughout tor compression? At the surface the density = that of ainiosphore, and 33 feet of water are equivalent to one atmosphere ; .'. at depth of 33 ft. the density = twice atmospheric pressure, (2 X 33) ft = three times (769x33)ft = 770times /. the density will be equal to that of water at a depth of (769 X 33) ft. i. e., '2i>371 ft. • It was proved by the independent researches of Marriotte, a French Physician, and Boyle, the Enpli»K Philosopher. 6—2 f 84 ,' f n ,» 'I i If MIS CELLANEO US EXAMPLES. 2. A body weighs in air iomnrs in wniAr -mn .»..» Z In water tlio body lose, (l 000 - 300) grs.. /. 0, 700 grs in other liquid /j^^,. ,,,., . ' .'. equal v..lt]me.s of water and of thn nth.,^ 1; • 1 «pectively 700 grs. and 5.0 gr" " ^"^'"^ ^^'^'^^^ ^^- •■• "^°^^^»'*^ «f «P^cinr gravity of other liquid = ''^^ = -6^857] -i. in^aMe u the pressure tmce what it is at a depth of on. Pressure at tlio surface = weight of column of wnter 33 ft. hi^h ..for a double pressure we must take 3(5 feet lower thatis 3b teet lower than 3 feet, or 39 feet from the surface ' 4. A Jlat piece of iron, ^,:eicjhiug 3 lhs.,fiuats in mercury; and if another piece of iron of like density iceiyhing 2 1. lbs.' is placed upon it, the j nece is just immersed. CoLara the ,pecijic gravities of t. ^ and mercury. Compare Total weight of iron = (s-f 2 |. ) lbs. = .5 ^ lbs. Tlie volumes of the part immersed and of the whole will be as the weights, that is, as 3 : 5 A ^ or as 78 : 135. .'. 8p.gr. of iron : sp. gr. of mercury = 78 : 135, = 2() ; 45. 5. Air is confined in a cylinder surmounted hy a piston without rcnght ^^.hose area is a square foot. What S must he placed on the pi.ton thai the volume of air Zy I reduced to half its dimensions? ^ will^hafe'dtble'ilr "• ' '^J' ^^''^'" '''^''''^ '' ^'^^ '^'' ^'^^'^ will lla^e double its original pressure. Hence takin- 15 lbs per square meh as the original atmospheric pressure, it be.* MISCELLANEOUS EXAMPLES. ^5 i comes 30 lbs. per siintiro incli below the piston. But the ut- niosphero still exerts a pressure of If) lbs. i)er squiire inch above the piston. Therefore a pressure of in lbs. moro per square inch is required to keep the ])iston at rest. /. weight requircd=(15 x 144) lbs. = 21G0 lbs. 6 If the mpacitf/ of the receiver of an air-pump he 10 ti?nc,s that of the barrel, sheic thai, after n strokes of the pistoji, the air in the receiver will have lost nearly one-foarth of its density. By the forn ^a of Art. 72, if po ^i'^^ Pn bo the densities originally and alter the m^'' stroke, and R and B be tlio capa- cities of the receiver and barrel, Po P3 Po D„ _ / R \n /_u)_Y^iooo, VlO+ V ~ 1331' ,-. density lost = (l - -^^j po= ^^Po = ^Po nearly. 7. A block of wood( s. G. -"j loclghing 156 lbs. is float- ing in fresh water. What weight placed on it will sink it to the level of the water ? Let x = \X\Q weight in lbs. Then x -v 156=-wei-ht in lbs. of water displaced by volume of wood alone, 13 ._ = 169; .*. ^^(169-156) lbs. = 13 lbs. 8. In a mixture of two fluids, of ichich the specific gra- vities are 3 and 5 respectively, a body, whose s. g. is 8, lo&es half its weight. Compare the volumes mixed. Weight lost = weight of fluid displaced, = ^ weight of body whose s. G. is 8, :, S. G. of the uaxture is 4. ^a^ IMAGE EVALUATiON TEST TARGET (MT-3) 1.0 I.I 1.25 ■- IIIIIM |50 '""^= ;i' m ||M 2.0 1.4 ill 1.6 6" P>2 ;^ <P» Am.. V. Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 8/2-4503 <^ iV M ^ A \ ls!.< I . I |. ::r 'I : I 86 MISCELLANEOUS EXAMPLES. 9. ^4 ^•^6•*^<? r/ «^-a^^r A^^ for its horizontal section a rect- angle 6 feet hy 2 feet. A substance ^ceighing 550 Ihs is im-. mersed in U, and the water rises 8 inches. Find the specTtic ramty of the substance. ^ -^ Sectional area = 1 2 square feet. Volume of substance = ( 12 x ?) cub. ft. = 8 cubic feet ; .\ 8 cubic feet of the substance weigh 550 lbs. • 550 .'. 1 cub. ft. 8 lbs., or 68-75 lbs. Also, a cubic foot of water weighs 62-5 lbs., .-. sp. gr. of substance =. ^^ ^i-i 10. A cylinder floats in a fluid A with one-third of its axis immersed, and in another B with three fo7irths of its Mixture ofequcd columes of A and B? Sp. gr. of^ : s|). gr. of ^ = 4 = }) 1 3' 4; .*. sp. gr. of mixture of equal volumes = ^ = 6-5. If therefore the body has \ of its axis immersed in a fluid of S.G. 9 when it is immersed in a fluid of s.a 6-5 the mrt immersed is obtained from the following relation, where ^ is the part immersed, 9 X t) X. 1 6 13 MISCELLANEOUS EXAMPLES. 87 100. We shall now give a sot of easy Examples to bo vrorkcd by the student by way of practice. Examples. — VIII. 1. An iceberg (s. G. -925) floats in sea-water (s.g. 1'025). Find the ratio of the part out of the water to the part im- mersed. 2. . A body floats in a fluid (s. g. -9) with as much of its volume out of the fluid as would be innncrscd if it floated in a fluid (s. G. ri). Find the specific gravity of the body. 3. Find the Fahrenheit Temperatures corresponding to -40" and 4-3r)0'' Centigrade. 4. The capacities of the barrel and receiver in a Smea- ton's air-pump are as 1 : 3. A barometer enclosed in tho receiver stands at 28 inches. What will be the height after three upward strokes of the piston ] 5. Two hydrometers of the same size and shape float in two different fluids with equal portions above the surfaces, and the weight of one hydrometer : that of the other = 1 ; ??. Compare the specific gravities of the fluids. 6. A man weighing 10 stone 10 cz. floats with the water up to his chin when he has a bladder under each arm ecpud in size to his head and without weight. If his liead be one- twelfth of his whole bulk, find his specific gravity. 7 At what height does the water barometer stand when the mercurial barometer stands at 28 inches (s.g. of mercury -=13-6)? 8. What degree Centigrade corresponds to 27'' Fahren- hei;.- ? 9 A man G*feet high dives vertically downwards with hia hands stretched 18 inches beyond his head. What depth has ho reached when the pressure at his fingers' ends is .^ that at hia feoti t 8S MISCELLANEOm EXAMPLES. I . P: 'J ir S it ■Si ^ :^ ' ( 10. . A stringf will bear a strain of 10 lbs. 7 oz. Dotor.'iiine the size of the largest ricco of corii (s. g. -21) wliich it can keep below the surface of mercury (s. g. 13-6). 11. In De Lisle's Thermometer the freezing point is 150" and the boiling point zero. What degree of this thermometer corresponds to 47" Fahrenheit? 12. Cork would float in n atmospheres. Find n (s g of air and cork being -0013 and -24}. 13. An elastic body of s. g. "5 is compressed to ^^-- of 20 + 4>i its natural size by immersion 7i feet in Tvater. At what depth will it rest? ^ 14. If the body in Question 13 weigh lOlbs., what are tho magnitudes and directions of the forces which will keep it in equilibrium at deptlis (a) 5 feet, and {(i) 30 feetr 15. At what depths will the force required to keep the body in Questions 13 and 14 at rest be 1 lb. ? 16. At what temperature are the readings on Reaumur. Centigrade and Fahrenheit proportional to 4, 5, 25 ? 17. At what temperature is the sum of the readings on Keaumur, Centigrade and Fahrenheit 212 1 18. A body (s.G. 2-6) weighs 22 lbs. in vacuo and another body (s. G. 7-8) weighs n\U. in vacuo; and their apparent weights in water are equal. Find n. 19. Find the specific gravity of the fluid in which the apparent weights of 1 lb. of one substance (s. g. 3) and 3 lbs. of another substance (s. g. 2 25) are equal. 20. Equal volumes of two substances (s. g. 27 and 6-1 > are immersed in water and balance on a straight lever 71 inches ong. Find the position of the fulcrum. ,. J^^' ^^^ proceed witli some examples of somewhat greater difhculty than those already given. Note. We shall assume that the volume of a sphere Is .rrrr^, r being the radius MISCELLANEOUS EXAMPLE^. 89 Dotcrniine b can keep int is 150" rmomoter n (s. Q. of 20 + w tiat deptli it are tlie icep it in keep the leaumur. dings on another ipparent liich the 3 lbs. of 6*1) are 1 inches greater )here is Examples worked out. 1. Shew how the deplh of the descent in a Dimng Bell can he determined from ohservalions on the barometer. A H y D Let AB be the surface of the water, CD the water level in the bell at the end of the descent. Now pressure at CD is equal to pressure throughout the upper part of the bell, and is therefore equal to the pressure due to atmosphere -1- weight of column of water {x-^y) ft. high. Hence if S be the measure of the specific gravity of mercury, and h, h' the measures of the heights of the mercu- rial column at surface of the water and at the bottom, measure of pressure at CD = hs + {x + y)xl. But measure of pressure at CD^h's \ :. hs + x + y = h's, .-. x={h'-h)s-y. Now, by Marriotte's law, if a be the measure of the height of the bell, ^=^„ or, 2/ = ^-,«; .-. x=ih'-h)s-- V a. ! 1 ' • f i |: ' 1' ■ fvi- ■j,t i i, j • ';i .'k I' ' 90 MISCELLANEOUS EXAMPLES 2. rr//^^ m^<5^ U the least size in cubic feet of an inflated balloon, that it may rise from the earth when filled with gas whose specific gravity com2mred with that of air is -08 the tceight of a cuUcfoot of air being •;} grains, and the collapsed balloon car and contents weighing altogether 550 lbs. F T'lking 1 as the measure of the specific gravity of air ^"^ ^ ofthevohimeoftlieiiiflatcdbulh.oM. wciglit of inflated balloon, ) neglecting weight of envelope, j "^"^^ ^ ^^ "^^ ^^^• weight of air displaced =(.Fx 1) grs. = Tgrs. Now 1 cubic ft. of air weighs '3 grs., •'• ^ 'SFgrs.; .'. ascensional force = (-3 F- -08 F x -3) grs. = (-92x-3K)grs. .'. •92x-3r=5r)0x7000, • • ^= .92 X -3 ^^^- ^- = Q^72-5 cub. ft. nearly. 3.^ The weight of a globe in air is TV, and in water w ; find its radius, supposing s and a to be the specific gravities of water and air. Let ^ = radius of globe, and P = weight of globe in vacuo. Then volume of globe = . ttR^ ; .-. P- irR'a^ W P - ttRH = w o (1), (2). Hence, subtracting (2) from (1), ■^■7TR'{s-a)=^lV^W]' ^ (47r s — a j AflSCELLAJVEOUS EXAMPLES. «•«•' an inflated d with gas r is -08, t/te \e collapsed s.r >f air, :edbullfiorj. gra. = Fgrs, 4. HoiD deep must a cylindrical diving hell he submerged fo as to be just half full of water ? At first tho bell is full of air of ordinary density. When the bell is half full of water, tho air is compressed into half its original volume, and therefore the density is doubled. But tho additional density is entirely due to tho weight of a column of water 33 feet high. Hence when the surface of the water in the bell is 33 feel Ijelow the upper surface, the bell will be half full of water. 5. A spherical balloon is to he formed of a material oj trhich the thickness is k, and specific gravity relatively to air 8 ; if it be filled with gas of specific gramty d, prove that it> order that it may ascend the extreme radius must exceed cater w ; gravitiei n vacuo. — V -d)' I^et ^ = extreme radius. Then a; -« = interior radius. 4 .*. weight of envelope alone - tt [a? -{x- xf) h ... (1), o gas ~ 'jT{x — Kfd air displaced (2), (3). The balloon will not ascend unless the sum of (1) and (2) be loss than (3). .-. ^'n{a^-{X'-Kf}b^\ir{x-Kfd-\TTx''\Q&s than 0; 3 o " .-. a?3 (8 - 1) less than {x - Kf (8- d\ ,\ l-*greater thanf g— -,y, r r ' 'A f 1* 1 f • Ih 1 1 . i ' i ' ,■' '','• .. 1 i' '1 .■: r ft 92 MISCELLANEOUS EXAMPLES. .-. ^Ie88thaul-^3_|), /. a? greater than < m- 6. J^or tico given temperatures the readings of one tJiermomeler are n^ and m^ and of another v^ and yf respectively. Wliat will he the reading of the latter when the former gives ^' ? (w — in) deg. of the 1st are equivalent to {v — /x) deg. of the 2ivd. 1- 1st, 1st I 2nd. 2nd. 7. A globe, 2 feet in diameter, when boating is half im- mersed in wat^r ; what is its u eight ? The globe must be half as heavy as water. 4 Now volume of globe = tt cubic feet, o and 1 cub. ft. of water weighs 625 lbs. 4 / 47r\ .*. -TT cub. ft. of water weigh (6225 x —I lbs. ; 1 / 47r\ .-. weight of globe = - ( 62*25 x -^ I l^s. = 130-9 lbs. nearly. 8. A sphere whose radius is 6 inches and wsight ?5 Ih^t is suspended hy a string. Required the tension of the string/ when the sphere is wholly immersed in water. 4 /l\' TT Volume of sphere = 0^(0) ^"^- ^*'-= « ^^^ ^*' Weight of water displaced = ( ^ x 62*5^ lb». / TT \ ,«. tension of string =^ t 35 - ^ x 62*5 j lbs. -2'275 lbs. nearly. MISCELLANEOUS EXAMPLES. 93 75 of one v^ and fi* liter when of tlio 2r«d. 2nd. 2nd. J half im- nght ?5 Ih^ ' the string 9. A pipe 15 feet long, closed at the upper extremity ^ is placed vertically in a tank (f the name height, and the tank is filed toilh icatcr. Prove that if the height (f the tcater barometer be 33/A din., the neater icill rise '3 ft. Oin. in the tube. Let a7=nioasuro of height to which the water rijjcs in feot. Then 15 -;c = measure of space filled with air. By Marriotto's law, the pressure of the air inside may bo represented by 15-.^• 4 But this pressure is also represented by the measure of a column of water 33 ^ ft. + a column (15 -it) ft. 33 , + 15-.t? = 4 l5-ic 4' or o 255 4 /255Y _ 60G25 V 87 ~ 64 ' x- 255 ■ 8 '' 225 8 3 .-. ;r = 60 ft. or 3 - ft. 4 The first result is evidently impossible. 10. If a lighter fluid rest upon a heavier, and their specific gravities be s and s', and if a body whose sp, gr. is a- rest with V of its volume in the iqyper fluid and V in the lower, shew that V : V' = ^-a- : (x-s, weight of body = weight of fluid displaced, =sV+s'V\ .-. r(o— s) = ^*(«'-c-;, i II ,1^ ^ V I >) ■h 5 94 MISCELLA NEOUa EX A MPLES, EXAMPLKS. -IX. 1. E(iual volumes of gold (s.o. 19-4) and silver {9^.0,. 10'4) bahmco 011 a straiglit lever, (1) in vacuo, (2) in water, (3) in meieury (s.g. 1 ;}•:.). Find tlio ratio of the arms and position of tlio fulcrum in each case. 2. An inclined piano is immersed in a fluid (s.o. 3) and a body (s.o. 7) \vei<,diin<^ 7 lbs, in vacuo is supported on the plane by a horizontal force of 3 lbs. Find the ratio of the iieij^ht and base of the plane. 3. A balloon filled with Hydrogen (s.o. -07) just rises in air (s.a. 1). The balloon, exclusive of the Hydrogen, weighs lOcwt. If a cubic foot of air weigh 1-3 oz., find the volume of Hydrogen in the balloon, neglecting the volume of all else. 4. If the balloon in Question (3) rise and rest with its barometer at three-fourths of its original height, how mvich gas must have been expelled, and how much ballast thrown out '\ 6. Explain why the gas and ballast in Question (4) are expelled. 6. A cylindrical vessel is made of wood : the exterior radius is 4 inches and the interior 3 inches, the thickness of the bottom one inch, and the height of the cylinder 9 inches. It floats in water when the bottom is 3 inches below the sur- face. Find the specific gravity of the wood and the depth to which it will sink when a small hole is made in the bottom. 7. A piece of ice, supporting a stone, floats in a vessel of water. Will any change take place in the level of the v/ater as the ioe melts ? ^ 8. Shew that in a cylinder immersed as in Question (25) page 64, the depth of the interior surface below the exterior is a mean proportional between the height of the water in the cylinder and that of the water barometer. 9. A cubical water-tight box, whose edge is 1 foot, is sunk to a depth of 80 fathoms in the sea. Find the pressure on the top. Would it make any difference in the circumstances of the box if it were not water-tight ? sr (a. a. 10'4) ivater, (3) in mil position i. 0. n) and a [)U the pliino D iiei{^ht and ust rises in i;on, weighs volume of all else. )st with its how much last thrown tion (4) arc 10 exterior hickness of 3r 9 inches. )W the sur- lio depth to bottom. a vessel of f tho v/ater lestion (25) exterior is ater in the bot is sunk isure on tho nces of the MISCELLANEOUS EXAMPLES. 95 10. An elastic air-ti!|ht bag has forced into it air sufficient to fdl If) bags of tho same orignial si/.o. To what depth must it 1)0 sunk in the water tiiut it may return to its original size, the height of tho water-barometer being :5 i feet \ 11. A vosssel mado of thin heavy material and containing 7 a cubic foot of fluid, tho specific gravity of which is ^ , floats in water, tho surfaces of tho water and tho fluid being in the same horizontal plane. Find tho weight of tho vessel when empty. 12. In Question (11) if some more fluid of tho same kind bo poured into tho vessel, will tho surface of the fluid or that of the water bo tho higher ? 13. A cylinder 30 inches long is composed of lignum vitro in its lower half and cork in its upper half, and floats vertically in water. If the specillc gravities of lignum vitje and cork be 1-1 and 2o respectively, shew that the cylinder will float 20-25 inches deep. 14. Two pieces of cork, botli small but tho volume of one three times that of tho other, aro connected by a thread three feet long passing round a fixed pulley at the bottom of a tank of water 2 feet deep. Supposnig the specilic gravity of cork to be -25, shew that in tho position of equilibrium the smaller piece will bo totally immersed and tho larger piece half immersed. 15. Two reservoirs of water at different levels aro separated by a solid embankment, and a bent iron tube of adequate length is placed with an end in each. If tho barrel of an air-pump be screwed into an aperture at tho top of tho tube, sheu' that generally after suHiciently working the air-pump th^ water wdl flow through the tube from the higher reservoir to the lower. Under what circumstances will this fail to take place ? 16 Two bodies of equd volume aro placed one in each scale-pan of a Ilvdrostatic Balance, and are then innnersed in two liquids whicii are .uch that the bodies just balance each other: the liquids aro then interchanged, and it is found that the bodies balance when one of thorn is just half immersed. Find how much of the heavier body must be immersed in a liquid, composed of equal vohimes of tho two liquids, so that it may just balance tho lighter not immersed. I 9« MISCELLANEOUS EX/ MPLES. 11 r ■ is 17. A 8ij)lK)n AliC, cuch braucli of which is less than 30 inches h)ii^', is fille<l ^vith luercury juul botli cuds uro stopped. It is tli(>n phuetl with tlic end A in a howl ol' mercury antl tiio end C in a l)o\vl of water, tlio surface of the mercury being Inicer tlian tliat of the water and liiglier than tlio end C. If tlio ends ho Riniultaneously unstopped, shew that mercury will How through tlie tuljc into the water i)rovided that -, bo greater than - , z p z, z' being tho rospcctivo doi)tlis of the end G below the planes of the surfaces, and p, p' tiio respective densities of mercury and water. 18. The air-vessel of a force-pump is a cylinder of height <?, whoso section A is tlio same as tliat of tiio piston : the water lias to bo lifted to height h of tho water-b:irometer above tho l)ottoni of the air-vessel, by means of a pipe of section a and lioiglit/t : if, when tho pump commences worliiiig, tho water bo just below tlio valvo in tiio air-chamber, find after how many strokes, each of lengtlh^, of tho piston, tho water will bo at tho top of tho pipe. 19. A cylinder whose height is 8 inches, is floating with its axis vertical and its base 6 inches below tho surface of water : a wciglit of G lbs. when placed on tho top of tho cylin- di.r just brings the upper surface to tho level of tho water. Find tho weight of tho cylinder. 20. When two metals are mixed in equal volumes thoy form a compound of si)ecific gravity 9 ; when they aro mixed in equal weights they form a compound of spccilic gravity 8 -; find the specific gravities of tlic metals. ,21. A cylindrical jar can just sustain a pressure of 1G5 lbs. to the sqnai'o inch without breaking, and an air-tight piston which f:ts the jar is thrust down and compresses tho air in the jar. Find the height of tho jar, supposing it to burst when tho piston is an inch from the bottom of tlie cylinder, the pressure of atmospheric air being 15 lbs. to the square hich. 22. In Smcaton's air-pump if there be communication with a condenser through tho upper valve, and tlie capacity of tho cylinder be half that of either receiver .'ompare the pressures in tho receivers after two descents aiK ascents of tho piston. [1 i NOTES. 97 s than 30 3 stopped, •y and tlio ;iiry boinj^ ml a If rcury will the pianos I mercury f height <?, the water iibovc tho /ion a and ) water bo low many bo at tho .ting with surface of tlio cylin- ,ho water. inics thoy wo mixed uvity 8-; of 105lba. ^ht piston air in th© b wlien tho e pressure lation with city of the pressures e pistou. Notes. 1. Law IT., given on page 4, can bo deduced from Law I., but the method of reasoning is not adapted to an elementary treatise. 2. On pago 15 tho construction of tho cylinder and linos f), 7, 8, 9 are not neccsmrif to tho proof, for it follows at onco from Art. 34 that fluid i!'*os8uro at ^ = fluid pressure at D. 3. On pago 2 1 it might bo clearer if wo inserted tho sign X or the word times between VS, and (unit of weight) in lino 7, also between y and (unit of specific gravity) in lino 14, and so in several other cases in pages 24 and 25. 4. Tho first sontcnco in page 53 is not quito correct : it might better stand thus: "The exhaustion of the air is re- tarded by tho difliculty of making tho piston come into close contact with the valves at A and C, and it nmst always bo limited by tho weight of tho valve CA" 5 The Aneroid Barometer is so called because no liquid {^ privative and vr]pi<: "moist") is used in its construction. A metal cylinder about an inch in height, closed by an elastic piece of metal, is exhausted, and as the metal covering rises or is depressed, according to the changes of atmos|)heric pressure, it sets in motion hands like those of a watch connected with it. 6. In reading the descriptions of the Tumps in pages 67—71 the student must be careful not to derive any erro- neous notions from tho use of tho words S^lcti(rl-\^\\^Q. It is retained (perhaps not wisely) as a technical term, con- venient for distinguishing the lower part of tho pumps from tho barrel. 7. In tho description of tho Siphon on pago 72 it is said to be of uniform bore. This is not essential to the worlong of tho instrument, but it conduces to tho regular action ot it, and renders the explanation more simple. y. II. 'I j 1 . '■ f u> 98 -W" NOTES. It IS also stated on page 72 that the longer bnmcn must be outside the vessel. This is not necessary, for the instru- mcnt will work with the shorter branch outside, provided that the extremity of that branch be below the surface of the fluid. 8. To the Thermometers it might be well to add tha* which is called De Lisle's. This is much used in Russiau scientific operations. In it the boiling point is marked 0» and the freezing point 150<>. 9. It should be carefully observed that the freezing point of a Thermometer is found by plrxing the instrument not in freezing (catet , but in inelthig ice. I 1* i nc/b must 10 instru- provided urface of add that RussiaL >d 0", and ANSWERS. ng point it not ](n 1. 56f tons. Examples I. (page 8.) 2. 30 tons. 3. 29G29'62Mb8. 4. 1 oz. 5. 1 oz. e! The area of a circle whose radms is r is irr^, and tak ing v' as an approximate value of tt, the answer is 5587 B^wt Examples II. (page 18.) 1. 20 lbs. 2. 37iVlbs. 3. 7:6. 4. 9:8. 5 10 feet. 6. 12 lbs. 7. 9ib8. 8 Iton 7cwt. 3qr.s. 17 lbs. 9. 11 lbs. 12|oz. 10. 22500 lbs. 11. 1125^3 lbs. 12. 2 of its height. 13 Since tho external pressure on the cork increases with the depth, while the internal pressure is constant, the cork will be forced in when the former exceeds the latter. 14. 12s tons. 15. IS feet. 1. 165 lbs. 5. 5oz. 6. Iffoz Examples III. (page 27.) 2. 18:1. 3. 7V|oz. 4. 'S. 8. 7-776. •016w m 9. ri6. 10. -844. '\ 5 12. -cub. in.; -cub. in. 1 3. Volumes as 1 : 2, weights as i : 4. 11. 14. 14. 2 : 1. IK o4 7 16, 17. 9325. ^ •i. II N If U' I % , , i !; I t lOO ANSWERS. 18. If «fi, c?2, ^3 be the measures of the densities of the fluids, and d bo the inc;isuro of the density of the mixture 19. 8-241... 20. *802... 21. 18-41. 22. 1-61.. 23. 313. 24. 8-G... oz. 25. The volumes aro as 57 : 1, the weights as 2223 : 97. Examples IV., (page 42.) 1. 3-§ 2. 507870 tons. 3. three-fourths. 4. 4dwts. 20i§grs. 5. 4. 6. 3 times weight of tub. 7. two-thirds. 8. --^oz. II. 42 oz. 80 ^' 432^"' 12. -^oz. 13. ^^Ibs. 14. 3-5. 10. 3 oz. 15. 20. 73* 16 19* 24. 12 feet. 16. l 17. 75 91 18. 17f. 19. 2f 21. 1362 2731 22. 2. 23. 47Mbs. 25. -66. 26. Because the specific gravity of salt water is greater than that of fresh wattr. 23. 1728. 29. 7 lbs. 9jVoz. 30. Edge of cube is 2 feet. 31. r/f}. height of triangle oo , / , ""/S ' ' ^^'"cn vertex is downwards ; 3 : 4 when vertex is u^nvards. 34. 16 lbs. 35. -75. 3G. 2 inches. 37. 9 27. " ' inclies. b.i 38. I^inch. 30. 4 lbs. 40. 3 lbs. 41. 95 lbs. 42. u^iiL^-w) '.w,,{u\-w). 43. Increased, if t;.c3 wood be lighter than water. 44. 3 : 2. 4,"). I'l. 141''9 47. Yff^ ^^ '^ nearly. 48. 6^*^ inches. 49. 8i«lbs. 50. 9?i^lbs. 61. 10|ft. 62. li •03. 6 inches. 55. 2?-. .^ 86400 , . ''^- -2053'""^^ "^* 67. rrr-, of a cubic yard. IJfK es of the I mixture, 1-61.. 3 : 97. ANSWERS. lOI 58. - of volume. 5 59. 750 oz. 85 61. 936302451-687 cub. ^^ 64. 900 grains. 67. 433 graius. 60. :^ of a cub. ft w 62. — . 63. m : n. 64. 900 grains. 65. l^J^ or 1-0272 nearly. 66. '64 • 69. 42^V^cub.m. Examples V. (page 60.) lit of tub. LO. 3 oz. 5-5. 19. 2f •s. 5 greater >jVoz. ertex is ) lbs. inch. , if t;.o 1 :j. 64 times 1. Den8ity = (^^y times original density. .. g^ . . , Q o • 1 4. No . because the ongmal pressure. 3. J . i. **• , .. ,,,p.„„„t:o,. pressure varies with the depth alone; so that if ^^^ ^^^ varied there would still be equal vertical increments of space for equal increments of pressure. 5. 1 J.1 a 11" inches 7. The mercury ^vould fall to the level of I'i ":^te i„ the cup. 8. U-«-25 lbs. 9 1« cet 10. No : because a volume of mercury equal to tot displaced by the irou will desceml --^ -""^ "\'; .t' its place without disturbing the ^'"'"'''''^^^''^IZ ZlZv 11. Siuk: see answer to (16). . 12- ''"''"'''iioa would descend a little. 13. 2-38 square inches. J". 09 . . , 1 1 f; 1 ff^ 'i^^-'.^- m 16. vv nen of oriffiuil volume. !»• i it., o^ ;.,;-, f i"- he ifoatiug body is partially i»"7-;'> ''".?-. ^H, are d' laced: but the aW««! weight ot floatuig ''O^S -™S' "^ of displaced fluids, which n.ust therefore be constant : there f„r. when the barometer rises, there must bo a los» water displacement, i.e. the body rises: «•'»'« ^^ f^Xneces" utn>osphoric pressure (when the '^'"•<'»'='« .''"-^V \ TClv Ute a'n merited water displacement, and the^lore tl.o body then sinks a httle. w. i • ^• 22. 26 \i- inches. 23. 5 feet. 21. lOSOlbs. ^■^- — 1 . . J ox c ' \ 25 The air will be compressed mside, and :o dispiace less waier •. and since it floated originally, it will now S^^^ . becauso the weight of displaced fluid is nowle.s than Z weight of the body. 26. 5 times o-.nnd pi-c.sure. , - . 00 Thf* ^nace between zero 'SI. ;..o. i02 » I I • ANSWERS. point and any graduation ought to bo loss than the spa^ t- indicated by the number i)hiced against that graduation in the ratio j^f 17 : 18. 33. 14-935 lbs. nearly. 34. yo of an inch. 35. Low. 36. 4t inches. .( 1 : i r < ii It Examples VI. (page 75.) I. It will increase the time of filling the receiver, since the only effective work would be done by the descending piston, after passing the hole. It will fill the tank in 3 tinie'^ the original time. 2. 27^ lbs. 3. (a) If the hole be below the level of short end, nv. effect. O) If above this level but still in the long branch, all the fluid in this branch below the hole will descend, and ail above in the same branch will ascend causing the rcmaindti of the fluid to flow through the short branch, till the siphon is emptied. (y) If in the short branch, all the fluid below the hok' is this branch Avill descend ; all above in the same branch will ascend and flow through the long branch, emptying the siphon. (5) If at the top of the siphon, the fluid will desceml in each branch and empty the siphon. 4. 32 ft. 9-53 in. or 327.9416 feet. 5. The fluid would descend in each branch and the siphon be emptied. 6. Equally well at both, if the siphon be not too high. 7. No: because the hold is lower than the surface in harbour. 8. 33 ft. iriin. 9. If the air be removed from the siphon, the fluids would first ascend in each branch and after- wards flow as usual. 10. The water would rise in the in- verted tube as high as the top of the inserted tube and afterwards flow out of it. 11. First, the water would soon cease to flow. Secondly, it would rise in each branch, and afterwards flow. 12. (a) The water will flow into the lower vessel. (/3) The water will descend in each branch till it stands at 34 feet above each surface, (y) The same as \_a). J 3. Each branch 2 feet. ^l iNSM^ERS. 103 the spat'j luiitiun ill iiii'ly. 'S. iver, sunt' escendiii-^- in 3 i\m^ir^ t end, (K! ranch, all :1, and ail cmaindti' le siphon r the hok' •anch will ying tho I descend lid would high, iirface in Tom the nd after- n the in- iUbe and uld soon nch, and into the anch till lie as i,u^. Examples VII. (page 81.) 1 n^ _lio. _80 (2) nf^ ^^ (3) ^^ '^' r4^ -17 0. ^^ '* (5) -2li; -Vl^. (6) -^^^ "^^B; trs U'. -1120 ((J) 150^ 302°. 3. (1) bO, , 1^5 • 2 m0;'360. (3) ^^ B80.' (4) 320; QO. (5) 5^; -120^ fl _ \lo. _ic)io/ 4. Yes: if the graduations are to be unifonn.^ ' 5. lo^ Cent, and 51.« Fah. 6. W Cent, and 50°Fah. 7. -400. 8. Make each degree -ths that on Fahrenheit. 8. 25^- 10- 20" Cent, GS^ Fah 11. O^". 12 The graduations would be inconveniently small. ?■ 800 Fah 14. 200 Cent, (>S0 Fah. 15. -1 If Cent., U^fI 16. 240. 17. 230. 18. 59^oFaim20Reaun..; if d be the number of degrees, Fah. rises -|- and Reaum. --. Examples VIII. (page 87.) 1. 4 : 37. 2. -495. 4. 11-8125 inches. 5. \ : p. 7. Sift. 88 in. 8. 970 10. 80 ''''^•^^' 13. 10 feet. 3. -40° and 6620. 6. 1-083. 9. 22ift. 2400 13"' 14. (a) 2 ^ lbs. downwards ; 11. 137F. 12. 0) 2 ^ lbs. upwards. 16. 600 Fahrenheit. 9 18. 15 17' 19, 15. 7 2^-5 ^^^ 13 4^^ 17. 1220 Fahrenheit. 2. 20. 17| inches from one end. Examples IX. (page 94.) 1 n^ 97 • 52 (2) 92 : 47. (3) 59 : 90. 1; (3) fulcrum is at one end, and gold between fulcrum and silver. I I I 1 r f ; V. ;• ¥ r' H ^' , fill ft li I' I :< i 104 ANSWERS. 2. 3:4 Q 10x112x16 ^^ 1-20 4. ^ of the gas 1 has been expcllocl, and - of the whole weight thrown out. 5. Gas to preserve equilibrium of internal and external pressures on the balloon. Ballast to preserve equilbrium of vertical pressures on the balloon. 6. Sp. gr. = ^ . Height immersed = 5 - inches. 7. No change will take place till the stone falls from the ice, it will then displace less water than before, and the sur- face will consequently sink. 9. Taking a cubic foot of water to weigh 1000 oz., the resultant pressure is 30000 lbs. The pressure would be the same inside as outside. 10. 102 fathoms, surface. 11. 125 oz. 12. The fluid 16. ^-. 19. 10 lbs. 22. 33 : a 18. A (2h + c- Jc"" + 4 A^-) + a { >Jc^ + Ah^ - c) 20. 10 and 8. 2AI 21. 11 inches. li.i »iiMiT I I if the gas out. exterjial ibrium of from the the sur- oz., the L be the :he fluid ics. One of the most popular Text Books ever published. NEW ELEMENTARY ARITHMETIC ON THE UNITARY METHOD. By Thomas Kirkland, M.A., Science Master Normal School, and William Scott, B.A., Head Master Model School, Toronto. Intended as an Introductory Text-Booh to Hamhlln Smith's Arithmetic. Cloth Extra, 176 Pages. Price 25 Cents. Highly recommended by the leading Teachers of Ontario. Adopted in many of the best Schools of Quebec. Adopted in a number of the Schools of New- foundland. Authorized by the Council of Public Instruc- tion, Prince Edward Island. Authorized by the Council of Pnblio Instruction, Manitoba. Withi)i one yehr the 40th thousand has been issued. ADAM MILLER & Co.,-' Toronto. \ 1 » i ■ r' HI fs. I Uighly Commended hy the Press of Canada and the United States. " ThG -Ith Edition. 50th Tliousaiul iHsuod within nine niontlis. Authorized by the Education Department of Pnnce Edwr.rd Island, introduced in many of the principal Public Schools of the Pro- vinces of Ontario and Quebec. elementarTarithmetic ON THE UNITARY ME HOD. By Thomas Ktrkland, M.A., Fcionce Master Normal fecnool, Toronto, and William Scott B A Head Master Model School, Tor> nto. * ' Cloih Extra. 176 papes. Price 85 cents. A. B. WESTEHFELT, H.M. Mt. Forest. exc Model School, Kirldand & Scott's^Eieinentary Arithmetic is an icellcnt work. It is intensely practical SAML. E. BROWN, Head Teacher, Sep Schools, Ti London, Ont. K^- rlum,iTI?Jl??; oxaniiued your Elementary, (by Ivnklnnd & bcott) and I consider it far superior to any other book of the kind with wliich I am ac° quainted and just what we require for onrTnior classes. I will introduce it immediately. '' ST, MAEY'.S ARGUS. The arrangement of the work is thoroughly ration- al, the oral and slate exorcises are exactly what is needed, being sumci.-ntly simple and yet wl 1 cal- culated to develop tlie thinking faculties while the wovVhr„n the simple and Uniform system of m ,1 pi^thl F^'^V^^""^ '^y analysis and deduction n) +1.1 -^ book correspond with the method of teaching arithmetic now beinc adontpd by all iutelUgent teachers. ^ aaopted EDUCATIONAL JOURNAL OF VIRGINIA This volume presents in a condensed form" all that is needed in an elementary book. Th^^S'^^^T^^^^'.^^^'^^^^ Granby Academy. qpott S !i^?''H'"^i Arithmetic, by Kirkland and Scott, IS estimated so highly by me, that I shall At:^^u.T^}''^^ ^\''^% ^° '^^^^'^ '* introduced into the t ly A\ oik, there is no text-book in use which equals .It in all that is necessarv both fr™the standpoint of the teacher and pupil. KIRKLAND AND SCOTT'S ELEM. ARITHMETIC. SCHOOii BULLETIN, Syracuse, N. Y. > Wo thiuk tlio book is oue of decided merit. A. KENNEDY, Head Master Martintown Model School. I consider it the best contribution to arithmetic which hiiH boon marie of lato years. The arrange- ment of tho work in oxcollont, the exorcises being well adapted for boj^inners, each series preparing the pupil for the next. GEO. B. WAED, M.A,, Head Master H. S., Orillia. I have used the work with private pupils pre- paring lor the entrance examination, and have derived much satisfaction from the plan ol the subjects and the exphiuations therein. The method of reasonina adopted afforded creat pleasure to the pupils also, who tiius seemed to be able to dispense with much oral instr-ction. The miscellaneous examples and tho hints fo. ivork- in" some of thom are very valuable. I speak ol wapils drspensing with oral instruction, not that this is advisable, but merely to 8^.>.ow that the methods are so clear that alter following the ex- planations tlie pupils were easily enabled to work out mentally any given example. A. C. OSBORNE, H. M. Model School, Napanee. I do not hesitate to pronounce it, as far as I am capable of judging, a vast improvement on the text- books heretofore used. Considerable prominence (though not too much) has rightly been given to the ''Unitarv Method" nnd tho method of enunciating principles by example and deduci g the rule there- from, backing them up by the vast ">J"'^e,^' «* l^^l'^^' tical nroblems, materially enhances the value of the work I ifke very much the style of introducmg practical problems from the beginning. A.D. McQUAKBIB, Hearlmaster Valleyfleld Model School, Quebec, The Elementary Arithmetic is just what is re- quired, and I believe will be, in the liand of an experienced teacher, far superior to anything A\e Jiave had. The Daily Expositor, Brantford, Ont. Kirkland and Scott's Elementary Arithmetic is a biglaly practical little bock, intended as an intro- ductory text-book to Hamblin f^mith's Arithmetic. The authors are well known for their l^g^Y.Sf h^ in scholastic circles and practical knowledge ot the teaching profession^ f It » I r ! ii t II I KIRKLAND AND SCOTT S ELEII. AIUTILMETIO. A. C. A. DOANE, InRp.,Rholl.urnn Co., No» a Scotia. I am much ploiiHoil with tho Kloiuoiit iry Arith- metic l)y Kirkland iV: Scott, it is oiio of tlib host of tlu) liiml I have Hoon. Tlio (ItiHiiitioiis ami oxphina- tioiiH arc fiimiilo and may bo ousily untl(»r8to(i(l, tlie mental oxorcisos and problems aio calcuiatod to do- velop thouf^ht and hIiow tho practical nHcH of tho scionco, tho roviowB toad to ])i-odnco th'ivdUi^hiicHfl, and tlio examination papcrH Ktsrvo t,o test tho pupil's capacities and tho oxtunt of their iic(piisiti()n9. On the whole it isadmini.blyadaijteil to tlio elementary departments of our common schools, and as such deserves to come into general use. A. ANDREWS, Hoad Masu:- NiiiRara H. fl. Tho Elementary Arithmetic will seiw. ..., .u capital introduction to tho Canadian Eiiitiou of Hnmblin Smith's Arithmetic. These two, aloii'^ with lOxami- nation Papers by McliOilan ife Kirkland, and tho Mental Arithmetic by Dr. IVIcLollaii, hxivo touchers notiiiiiR more to dosiro in tho way of text-books on this subject. Tho Dumfries llrfomier, Ont. The avrangemcnt of tho work is thoroughly rational, and the ornl and hlato exorcises uvo < xiict- ly what is needed, beiiij,' sullirientlv simple and yet well calculated to ilevelep the thiiikiiif^ fucultioa, while the adoi)tion of liie simple and nnif.rm sys- tem of working all proldems by analysis and deduc- tion makes tho bc.jk correspond with the method of teaching arithmetic now being ail()i)ted bv all intel- ligent teachers. This mo,st excellent littlo book det:erves general introducLion to the junior depart- ments of our common schools. J. F. JEPFERS, M.A., H. M. Coll. Inst., Petnvboro^ . The Elementary Arithmetic bv Messrs. Kirkland & Scott is valuable for its simplicity of definition, omission of things obsolete, and for the rational, practical nature of its examples. T. L. MICHELL, B.A., H. M. High School, Perth. I have made a careful examination of the Elemen- tary Arithmetic by Kirkland & Scott, and have no hesitation in attesting to its merits as a text l)o<)k, both in rospect to matter and tlie luaniier in which the different steps are introduced. It is a good juo- paratoi-y boolc to Haniblin Smitii's Advanced AriMi- metic. and as such siiould be introduced into every public school in the land. E. ALEXANDER, H. M. G.alfc Model School. I am plaased with the arrangement of tlis subjecta and the practical character of tho problems. It iij very suitable for junior classes. HAMBLIN SMITH'S MATHEMATICAL WOPtKS AU USBD ALMOST KXCLUSIVCLT In the Normal and Model Schools, Toronto; Upper Canada College; Hamilton and Brantford Collegiate Institutes; Bow- manville, Berlin, Belleville, and a large number of leading High Schools in the Province. HAMBLIN SMITH'S ALGEBRA, With Appendix, by Alfred Baker, B.A., Mathematical Tutor, Uni- versity Colloye, Toronto. Price, 90 conta THOMAS KIRKLAND, M.A., Scir o Master, Normal School. "It is the text-hook on AlgcV :i for candidates for second-class certificates, and for the Intormc .co Kxamination. Not the least valuable part of it is the Appeuc' by Mr. Baker." GEO. DICKSON, B.A., Hea jlastcr, Collegiate Institute, Hamilton " Arrangement of subjects good ; explanations and proofs exhaus- tive, concise and clear ; examples, for the most part from University and College Examination Papers, are numerous, easy and progres- sive. There is no better Algebra in uso in our High Schools and Collegiate Institutes." WM. R. RIDDELL, B.A.,"B. So., Mathematical Master, Normal School, Ottawa. " The Algebra Is admirable, and well odapteJ as a general text- book." W. E. TILLEY, E.A., Mathematical Master, Bo\vman^•ille High School. " I look on the Algebra as decidedly the best Elementary Work ou the subject we have. The examples are excellent and well arranged. The explanations are easily understood." R. DAWSON, B.A., T.C.D., Head Master, Hish School, Belleville. " With Mr. Baker's admirable A|)pendi\-, there would seem to be nothing left to be desired. We have now a first-class book, well adapted in all respects to the wants of pupils of all gmdes, from the beginner in our Public Schools to the mo.st advanced student in our CoUcnate Institutes and Uvxh Schools. Its publication is a great lx)on to the over-worked matbomatical teai^hers of the Province." I I I I" . II I r.i ^ i )*i Km 1 1 _ ft. HAMBLIN SOUTHS ALGEBRA. VViih Apncn.lix by ALFKKD UAKEH, D.A., Matheinaticiil Tutor, University C'lHejje, Toronto. 4th li^tl., go cts. Anthcrized by ttie Minister of Education for Onturio, Authorized <;;/ the I'.uuucil of Puhlir Iiintrni-tioii for Quebec, Hecammended by the Semite of the Univeraity of' Halifax. o 0. MACDONALD, Prof. MathemiitlcB, DallioviBlo College, Halifax " I have received a Bot of your Mathotiiatlciil I'lihlicatloiifi, viz., the TroiitlHOR on Arithniotic, Alt,'obra, luid (iooiin-try, by Mr. Hiuiib- liu Sinitli. Tiioy all Booiu to 1110 adiuirablo troiitis'es, and fUtod to be the text bf)()liH for inoro thoiou^jh atid RoloiitiCic touc'iiiif! tliun hu8 yot found Its way into the majority of our lu'^li hi^IiooIh and aciidoiiiiort. Of tlio coiiiouB oxoroiHoa in (iloinotitnry al^jchrnio, i)ro- cesHt'H every tlioroii-,'!! toaclior will a))i)it)vo, Kinco oxixnioiico sluiwa tliat, as dlHcipliiio in >,'raininar is the main roMiiirouKsnt of tlie yountjBtiidont of claHsicH, bo praotlco in aUtobrnic ninniinilatioua is the finidaiuontal ro<iiiiioniHnt of the nJii'bi-.iiHt. 'l'}ion a^jain, tlie refoi-onco of oqnatioiiH involving the trcatnjcuit of radicalH to a ■oparato and advanced Bootion, inarlvM t .0 antlior as one who lias ■lytiipatliy with the dillicnltioa of bogititierH. The oxposlMoiiR are uniformly fiucclnct and clear. Tijr i;..'onu!trv has moiits fninally hlRh. Manjy of Kuclid's mothoda ait iuiiirovod on, ami propositions, not as in hiiclid, dednccil from a common principU). 1 may instance two proposit ions In the 3rd book,thn2'2nd, and the :ilst. Tlio iiiuthod of Btiperpositiou of trianfiles emph-vod in tlio earli(n- proposiLionH of the Olh book, will b'j to many a strikinj;? novelty, and it i.s uniform Of conrHe, many of us, from long practice In expoundiii!,' and iiritj cising Euclid's olomout, had arrived long ago at these mctiiodi' Hut it may be doubted if they are generally known Tiicv ai „ mupiostioiinbly preferable to the old, though Euclid's mftltodn ought to bo explained along with them. We want sadlv a, nationa,| Euclid, and this is the best iipproximation to it thjit i have Komi. We in DalhouHio include these books as admissible and rcciom- mended text books iu our nuithematical classes of tho first year. They are sure to come iuto extensive demand, as thoir merits come to be recoynised. B, C. WELDON, M.A., Math. Master Mount Allison Collece. Sackville, N. B. Wo are using your Algebra in our Aca«omy.'' A. 0. A. DOANE, Inspector of Schools, Barrlngton, N. S. "The algebra as an elementary work contains all that is nooded for our better clasr, of common schools. The armngoment is such an to lead the studont from tirst ])riuciplc8 gradually to tho intri- cacies of the Bcit'iice, and then with lucid discusHions to unravel those intncacies and bring the whole under the comprohonsion of every ordinary intellect. The exaiuinatiou papers form a valuable and useful part of the work. I can unhesitatingly recommend it to teachers us > .11 adai ted to aid them materially in thoir work, and to Btudents r,- a te>t book weU suited to their needs. 0. T, ANl>I<Jii\v'S, Inspector for Queen's Co., N. S. "I have examined Hamblin Smith's algebra and found the ex- amples admirably arranged in a progressive order, easy and Avell adapted for the use of our public schools, into which I Bhall be pleased to recommend its introduction. HERBERT 0. CREED, M.A., Math. Master Normal Scotia, I'Tedericton, Is.B. "I have made sufTicient acquaiutance with Hamblin Smith's algebra to be satisfied of its excellence as a text book, and to war- rant me iu recommending it to one of my claues. i aticAl Tutor, frfo. >r Quebec. 1 1 ill fax. lloge, Halifax. licatloiifi, viz., by Mr. Miutib- , a!ul fUtoil to Loiic'iiiif; tlian li H(iho(ilH anil ilfjfhiiiic, j)ro- orioufo k1u»W8 oiiitiiit of the tiipulatiouH is ion nt,'iiin, tlie rtiilicalH to a H Olio who iias cpositioiiR aro lorits P(iiinlly 1 propositions, may instance i. Tlu! iiiuthod !■ propowitiona 1 it is uniform liii;,' aiKl critj. icHO nictliotlg_ n. Thoy ai ^ id's llW't'ltOllg lly a, national t i havo Konn. and THcioni- tho lii'Ht year. r moritscoino on College, on, N. S. ;}iat is nooded ouient is such y to the iiitri- )nrf to unravel prolicnsion of L-ni a valuable rocomniend it in thoir work, ids. N. S. fonnd the ex- oasy and avcII cli I Bball be lol Scotia, nblin Smith's k, and to war- THREE EDITIOiNS SOLD IN SIK MONTHS -OP— HAMBLIN SMITH'S ARITHMETIC, ADAPTED TO CANADIAN CUKRBMCT THOMAS KIRKLAND, M.A., Sclenoe xvTaBter Normal School, Toronto, and WM. SCOTT, M.A., Head Maater Model School, Ontario. 4th Edition, Price, 76 Centa. AutluyHzed by the Minister af Edueatinn, Ontario. Authorized by Ihe Council of Public Inatructiou, Queb4e, Recommended by the hknato of the Univ. of Halifax. Authorized by the Chief Supt. Education, Manitoba. FROM NOVA SCOTIA. A. 0. A. DOANE, Inspector of Schools, Barrington, N. 8. " Eamblin Smith's arithmetic seems very suitable to the necei- sitlea of our public schools. The exorcisos arc i^^l''''"' •'!«• '''"Ji*^^ examination papers are invaluable as aids to tcunhers m thorough tfaininff Thoy will also prove of groat son'ice to pupi s desirous ■ of passing the grade tests. The author appears not to volv so much Sn set nUes al upon explanations and tho clearing of seeming Sbs?urit 08, 80 that pupils may readily comprehend the questions and proceed to the silutions. I cordially recommend its use to all those desirous of obtaining an acquaintance with this branch of aseful knowledge. 0. F. ANDREWS, Inspector for Queen's Co., Nora Scotia. " I have much pleasure in certifying to the superiority of the Canadian edition olf HambUu Smith's Arithmetic over any text book on that subject that has yet come under my notice. It is practical, complete and comprohensive The appendix 'fd exam- ination papers are important and valuable^^features. I shaU be pleased to recommend its early introduction. W. S. DANAGH, M.A., Inspector of Schools, Cumberland, N. S. HAMBT.IN Smith B Arithmetic.— "It has a value for candidates preparing for public examination, as the examples have been mostly culled from Examination papers, indeed I may say that I have not seen any other workontliia branch that is «o socially calculated to assist the student in passing ^jth credit oi^ctaJi«at«. I therefore think that HambUn Smith's Arithmetic should be ploced on the autJiarized list of books for public schools. ! f' J! J EXAMINATION PAPERS m ARITHMETIC, s ^^m' -A.. MoLellan, LL.D., Inspector High Schools, and > Thos. Kirkland, M.A., Science Master, Normal School. | Toi onto. ■§ e PRICE $1.00. ^ e - '— « g e Prom the GUELPH MERCURY. fT «; * ,V !P^^, ^°^^ *^ divided into six chapters. The iirst is on the Unitary Method, anri given solutions showing, its applicvatlon to ! variety of problems, in Simple and Compound Proportion Percentage Interest Discount Profit and Loss ; Proportiona' Parts/l4r neSv S'nT ^"'«' „J?^«'?,^»ye, Alligation; Commission, 1. sura, ee ScT.' fetoclis and Miscellaneous Problems. The second is on Elenientarv Rules, Measures and Multiples, Vulgar and Decimal Fractions The third contains Examination Papers for entrance into High Schools and Collegiate Institutes, the fourth fur candidates for third-class ccrtii cates, the fifth for candidates for the Intermediate Exam nation ad second-class certificates, and the sixth for candidates for th rd-class certificates and U.nvtrsity Honours. It vill be observed that the wrk begins with the fundamental rules-thoss principles to be acnui rod when a pu,)il first enters upon the study of Arithmetic, and 2n-ries ^InZrii^'V'-^^'^'-?"^ *"^ ^^^ highest class of certificates and S Honours of the University. . . . Teachers will find in it a necessarv help in supplying questions to give their classes. Those who asiSe S 5L*!f;''^\T ^^V'^'^'l ^''^^^ ''^^'"^'• guide-indeed ^here is not soSd a one— on the subject with which it is occupied. From the ADVERTISER. *y, ' u ' ?y *" ''^° *'"® ff^'^PJ"? after some method better tlian they have at present, this volume will bo cordially welcomed aSd many who have never suspected the possibility of accon.S Sir so much by independent methods, will be, by a perusal of en troduc tory chap er impelled to think for themselves, and enabled to teach their pupils how to do so, . . . It is far buperior to amthin- of the kind ever introduced into this country. . . . The tv> o"rin v. n aj.pearance of the work is of a very higii diaracter-qiXtou'' i' arnSe^lI'^^ '''' '"'^'^ '' ^^^ ^-' publish Sui ^'i d <p a a o o a o • rH S-l a> a <! a o m a i— t ■o o From the TELESCOPE. . . . The plan of the work is excellent, the exercises heine arranged progressively, each series preparing the student for the next The problems are all original, and so constructed as to prevent the student using any purely mechanical methods of solution We should really feel proud of our Canadian Authors and publ'ishin- houses, when we consicler the infancy of our country and the progress it has made and is raaking in educational matters, and particularry it) the recently published education^ works. "wuuuij mj RS s 1I3, and g liool, ^ e PSA g 3 on the I n to a =. centage, "g iiersliip; qj Je, &c.,.S rnentary '^ s. The o )oIs and ^ ccrtili- rt ion and ird-class lie work .cquircd carries and for 'cessary spire to ) good a ra a o • rH (-1 a <! a o o ;r than ^d, and ling so troduc- teach ; of the ai)hical [ual, ui uses ol s being e next. mt the . We )lishin:j; •rogrcss lorly iu DR. MCLELLAN's mental ARITHMETIC. From the CHATHARi PLANET. This book will prove an important auxiliary In the study of arithmetic. A. C. HEREICK, Head Master of Public Schools, Coilingwood. McLellan's Mental Arithmetic, Part I., is every- thing tliat can be desirod as such. It should be in the hands of all teachers. Its Fource is a sufBcient guarantee for its thoroughness. I would be pleased to see it introduced into all our schools. R. KINNEY, M. D., -Insp. Public Schools, District No. '2, Leeds. Well adapted for use in our public schools. D. H. HUNTER, M.A., H. M., H. S. Waterdown. It is an excellent little work, which will supply a want lonp; felt by Canadian teachers. J, FRITH JEFFERS, M.A.. Coll. Inst., Peterborough. The Mental Arithmetic by Dr. McLellan supplies a want in our list of text-books. Ever since the introduction of the unitary method of teaching written arithmetic there has been needed such a guide in mental exercise. The methods of opera- tion and the character of the examples make the little book worthy of a prominent place in school work. W. H. LAW, B.A., Prin. High School, Brockvilla. It will supply a very great defect, and I am sure the profession will cordially welcome it. Rapidity with accuracv is not found in our schools, and the'Do' tor's excellent publication will admir- ably accompiish these results. J. H, McFAUL, H. M. aiodel School, Lindsay. It is a most excellent drill manual, and should be in the hands of every scholar. A. BOWMAN, M.A.,H.M. High School, Farmersville The Mental Arithmetic, like its author, needs no commendation. It was needed, and will bo much nsed. M. MCPHERSON, M.A., IT. S. S., Prescott. You certainly deserve the thanks of all who aie interested in the education of our youth, for your efforts to sup)ily our teaohors and pupils with suit- able text boMiS. I i-im pleased with McLellan s Men- tal Arithmetic, and hopo it will soon be m the hands of every teacher in this Province. Were mere atten- tion Given to m.'Tital arithmetic in the tinmary classes m our Public Scnools, there would be fewer failures at our second class and intermediate exa- minations. i I f r f ? l^ i ! 1 '^' ^ I i*' r ..i .' i . t * ^ t> ' f: •[ i! ' : ENGLISH GEAMMAK BY C. P. MASON, B.A., F.C.P., Fellow of University College, London, With Examination Papers by W. Houston, M.A. PRICE 75 CENTS. ALEX. SIM. MA., H. M., H. S., Oakville . Upwanls of three years ago I asked a gi-ammar school nepectot m the old country toHeud ino the best grammar ijubli he<? there. He immediately sent me Mason. A. P. KNIGHT, M.A., H.M., Kingston Collegiate Institute. Incomparably the best text book for the senior classes of our high schools that has yet been offered to the Canadian public. J. KING. M.A., L.L.D., Principal. Caledonia, H. S. Mason's gi-amraar will be found a niost valuable class-book ^b pecially for the msti-uction of advanced classes in EngUsh The chapter on the Analysis of difficult s-mtcncos is of itself bufflcient to place the work far beyond any EngUsh grammar hitherto be- fore the Canadian public. RICHARD LE\VTS, H. M., Dufferin School Toronto. As a philosophical treatise its discussion of doubtful points and Its excellent methods and definitions cannot fail to rive it a hi-^h rank m tile estimation of the best judges of such works— the scho^ol teachers of the country. It has reached a twontv-llrst edition iu England and I have no doubt it -win meet witli the same high ap. preciation m tins Pro%lnce. JOHN SHAW, H. I\r., H. S., Omemee. ,- '^* *^^'fso^'8Grarauiar is just such a book as many teachers nave been hoping to see introduced into our sobools, its method being to teach the subject by explanation, dcliuition and abun- dant illustrations without stereotyped rules thereby makiut' the study even attractive. D. C.MacHENRY, B. a., H.M., Coboiu-g Col. Institute. It is an excellent and reliable work. It will be well received by teachers and advanced pupils. JOHN JOHNSTON, P. S. I-.l^lleville and. South Hastings. Of all the grammars that I have seen, I consider Mason's the best. ^;. 0» •^~ L % ^ J. MORRISON, M.A., M.D., Head Master, High School, .Newmarket. I have ordered it to be used in tliis school. I aonsider it by far the beat English grammar for high school i)mn)osos that has yet appeared. With "Mjuion" and "liemiug" nothing more seema to be detired- TO AVOID CONFUSION, ASK FOB IIILLBU'S SWINTOIT'S LANGUAaS LESSOITS, The Blew Aiuaiorizccl Graanniar, fi!ILLEfi'S SWINTON'S LMGOIIGE LESSOiS, BY J. A. McMillan, b. a. The only Edition prepared as an Introductory Text Book to MasoWs GranimLur. In Miller's Edition of Language Lessons Tlie Dennitions of file Parts of ?»pcecli are noiv luadc ijJeiitical ^vitn Mason's GiaKaaiar. The Classiflcatlon of Pronouns. Verb", floods, and Cieneral 'I'realiueut are the same as iu Mason's TC-Xt Book. Miller's Kdltlon is prepared as an introductory Text Book for Mason's txrammar, the authorized hook for advanced clat^ses for Puhlic Schools, so that what is learned by a pupil m an cl.'mcn- tary text-book will not have to he unlearned when the advanced book is used, a serious fault with many of the graded Public School Books. Miller's llldition contains all the recent examination Papers set for admission to High Schools. MIIiliER'S SlVIIV'rON'S LA>'«UAGI': LESSONS is authorized by the Educatiou JJepartinent of *. mtario, is adopted by the SchooLs of Monire d, is authorized by the Council of Public Instruction, Manitoba. To the President and Members of the County of Elgin Teachers Association: ,,,,,, , \- e In accordance with a motion passed at the last regular meeting ot the Association, appoincing the undersigned a Comiuittoe to con- sider the respective merits of difterent Enghs.. Grammars, witli a view to sug;>-est the most suitable one for I'ublic Schools, we beg leave to report, that, alter fully comparing the various editions that have been recommended, we believe that " Miller's Swinton's Language Lessons" is best adapted to tlie wants of junior puyuls and ''would urge its authorization on the Government, and its unro- duction into our i'ublic Schools. St, Thomas, Nov. 3uth, 1878. A. E. Bin LEII, Co. Inspector. J. McLEAN, I own Inspector. J MILLER, M.A., Head Master Pt Thomas Hich School. A. STEELK, B A., •• A>liner High School N. M. CAMPiJELL, Co. of Kigiu IModel h^ehool. It was moved and seconded that the report bo received adopted —Carried unanimously. d Price, Olotli Exti'a, *"> ADAM MILLED & CO. rf!) Whole {Series in one Voiume Uomplete, $1.00. • i f n n :a H:.R The New Authorized Eleinentnry (irram in nr. MILLEri'S SWIHTON'S LAHSUACE LESSOHS. M[f>i.f:r's Swinton's Language Lessons is used exclu- sively in nearly all the Principal Public and Model Schools of Ontario. Among them are 4M(ana, HaiiiiKoii, >Vliitii^, I'oitUope, C'oboiirg, Alitclicll. A.. •aji'>e, SiraiUroy, ^indtor, Scaforiii, liniokville, JMcai'oi'd* tliiitou« Listowcl, St. i'nlharincs, Itrantl'ord, Fertli, Belleville. LiiKlsny, Uxbrldge. St. Tiionias, Braccl>rids<'« A(loi>(ed bj the Fi-otestant Schools of IHoatnal and Levi lolleso* Quebec, Mchools of IViiieiipc^, Itlanitoba, and St. Jiihu's, ^e^y Foundlathd- Resolution passed unanimously by the Teachers' As sociation, (North Huron), held at Brussels, May 17, 1878 " Kesolved, That the Teachers at tliis Convention are of opinion that 'Miller's 8\vinton Language Lessons,' by McMillan, is the best introductory work on Grammar for l^ublic School use, since the detinitions, chissitication and general treatment are extremely simple and satis factory." In my opinion the best introductory Text-book to Mason's Grammar. All ]3upils who intend to enter a Hiidi School or to become students for Teachers' Certiti- cates, would save time by using it. W. J. CAPtSON, H. M., Model School, London. The definition's in "Miller's Svvinton Language Les- sons" are brief, clear and exact, and leave little to be unlearned in after years. The arrangement of the sub- jects is logical and jDrogressive, and the book admirably helps the judicious teacher in making correct thinkers and ready readers and writers L. W. WOOD, 1st A Provincial H., F.S., Trenton Falls. Be carelnl to asU ?oi' H:ii!.s:K?s s^f 8M'0.\, as o:ii retiUi;;ns ill «■ in liic ittarkt-i. iiniiir. LESSONS. used exclu- and Model !'S, Mitchell. €nlharinos« intrord, lla, llcville. il and Levi Diloba, eachers' As ay 17, 1878 ntion are of a Lessons/ in Grammar lassitication e and satis sxt-book to to enter a lers' Certiti- :. M., , London. muasre Les- little to be of the sub- c admirably ct thinkers iiion Falls. i' J * In n.aking history attractive to the young the Author has proved his apti- tude in a di'piirtiucnt of literature in which f.'w distinguish tliemselvcs The uarativo is so sustained tliat those who take it up will have a desire to read it to the end.' Dundee Advertisek. THB EPOCH PRIMER Of ElVOLISn HISTORY. Being an Introductory Volume to the series of Epochs of English IJistoryt by the Eev. MANDELLCllEIGHT(.)N, M. A., late Fellow and Tutor of Mer" ton College, Oxford; Editor of Epochs of English History.' Ecp.8vo.pp- 148, price 30 cts. cloth. 'As all the leading features— political, social and popular— arc given with much impartiality, it can hardly fail to become a school class-book of great utility.' Wor.CEHTER JotTRNAL. ' The Rev. MANDKLijCKEiuirio:-; has really succeeded in making an admir- able resume of the wliole of tlie prin- ciple events in English history, from the time of the Koman Invasion down to the passing of the Irish Land Act in 1870. Interesting, intelligible and clear, it will prove of great value in tlie elementary schools of the kingdom; and those advanced in years might find it very handy and useful for casual reference.' Northampton Herald. ' This volume, taken with the eight small volumes containing the accotnita of the diifereut epochs, presents what maybe regarded as the most thorough course of elementary English History ever published Well suited for middle class schools, this scries may also bo studied with advantage by senior students, who will find, instead of the mass of apparently unconnected facts which is too often presented in such works, a careful tracing-out of the real current of history, and an in- telligible account of the progress of the nation and its institutions.' Abkudekn JOURNAIi. ' The whole series may be safely commended to the notice of parents and teachers anxious to find a suitable work on English history for their ' Tills volume is intended tobe in- troductory to the Epochs of English History, and nothhig co.d be better adapted for tiiat purpose. The little boolc is admirably done in all respects, and ought to have the effect of sending pupils to other and full( r sources of liistorieal knowledge.' Scots-man. 'Mr Chi iohton'^ introduction to the Epochs of English History covers in a hundred and forty pages more than 1800 years, but having regard to its extreme condensation is well worthy of notice. On the whole the work is admirably done, and it will no doubt obtain a very considerable sale.' ATIIENiEUM. *An admirable little book that can scarcely fail icr obtain a considerable popularity,! notwithstanding the great number of previous attempts made to relate the history of England in a very small compass — In this epitome the epochs become chapters, but an in- teresting account is given of such events as are likely to be attractive, or even moderately intelligible to young readers.' VVelsiiman. ' The excellent series of little books published under the title of Epochs of English History, edited by the Rev. MANDEiiii Creighton, M. A., and writ- ten by various able and eminent writers being now complete, the Editor has prepared an introductory volume, cal- led t>.o Epoch Primer, comprising a concise summary of the whole series. The special value of this historical out- line is that ii gives the reader a com- prehensive view of the couiso of mem- orable events and epochs and enables hira to see how they have each con- tributed to make tlio British Nation wliatit is at the present day. Literary Woeld. children, inasmuch as the several volumes are simply and intelligibly written,without being overloaded with details, and care has been taken to bring every subject treated on within the comprehension of the young. The namby-pamby element, which is so often conspiv;uous in histories for children is' entirely absent, and the works in question are certainly amongst the best of the kind yet issued. The little volume now under notice, which brings the series to a close, is fully equal in every respect to the preceding ones, and it will be found exceedingly useful to every one who may have to teach English history.' -^r^ Leamington Coubier. ' ^s ll ••Epochs in History mark an ^^^cn in the Study of it." ^ G. W. JouNSON, H.M.M.S., >£aimlton. An Acceptable Text-Book on English History AT LAST FOUND I EPOCHS OF imim history, BT REV. M. CREIGHTON, M.A. Autlioriz<od by tlie Education Bepartment. Adopkd by the Public ScJwols of Montreal, and a number of the best Schools in Ontario. " Characterized by Brevity and Comprehensiveness."— Canada Presbyterian. " Amongst manuals in English History the Epoch Series is sure to take high rank."— Daily Globe. *' Nothing was more needed than your excellent Primers of English History."— Fked.\V.Kelly,M.A.,B.D., Lect. in English History, Eligh School, Mont eal. In Eight Vohmes, 20 cents each, —on— WHO LE SEHIES in two VOLS. ONL Y 50c. each. Part E Contain First Four of the Series. Part IE Contains Last Four of the Series. - ^DAM MILLER «& CO. TOEONTO. t." iamilton. itory ORY, [.A. lent. umber of :ness." — e Epoch excellent .A..B.D.. lONTO. CHEI&HTON'S EPOCHS OF ENGLISH HISTORY ■o Ecv. Geo. Bi.aik, M,A,, I. P. S., Grcnvillo County. "This little work, published in tight miniature voUunos, at 2(Uj. each, is p( culiarly aduptid for u-^^e in our Public and llifth Schooli. Proaentfd in tbis simple and attractive I'orni, each of the great epochs of I'lnglish History can ho cheaply, easily, and thorouglily mastered before proceeding to the next." Thos. Carscadden, B.A., Head ]\lastei'. High School, Richmond Hill. "I can most cordially recommend thom to all students who are candidates for the Intermediate, or teachers' examinations." J. TuBNBVLii, B A., Principal Jligh School, Clinton. "I have examined the 'l':pochs of tiigl'sh History' and have formed a very higli opinion of them, so much so, that 1 intend to introduce tliem into the liigli Scliool here. A a to the si /.c and ex- pense they have hit the happy mean, containing all that is really necessary and nothing more." H. J. Gibson, B.A., Head Master, Renfrew, H. School. •• I have ciuefully examined your 'Epochs of History,' and be- lieve them to be admirably adapted for preparing teachers for certi- ficates. They are very neatly got up." John E. Beyant, B.A., Clinton. "I have been anxiously waiting for a Canadian edition of these delightful little books, and now that we have these, I shall introduce them into my classes as soon as possible." A. Ding WALE Forutce, P. S. I., Fergus. " I think it is a great mistake, at a time when imagination is pe- culiarly vivid, to expect history to be studied from the hare hones laid down, and that the little work referred to has been prepared in a simple, interesting way lor tliose eomniencing the study of history, and fitted to carry them on by the grasp th< y can take of the subject as it is presented, and as one event is connected with another, I think some such introductory work was much needed." J. M. Plati. M.D., P. S. I., Picton. '•Neatness of 'get up;' sin)plicity of langiuigo ; faithfulness of record; perfection in arrangement; interest of narrative ; concise ness and freedom from dryness ; or recital of facts, are but a few of the recommendations of these beautiful little works." P. H. Michel, B.A., H. M., H. S., Perth. "It has been said that a book that would sui)ply the place of 'Collier's British History' could not be obtained. This is more than answered by the ' i'lpoclis of English History,' They pro- ceed on the liasis on which history should be taught. Divisions are made according to the inception and cessation of those forces that brought about changes in the English Constitution, while principles are clearly communicated and systematized. Not beyond the capa- bilities of younger children, they are also adapted for use in higher classes.'' BOBT, RoLGERS, Inspcctor of Public Schools, CoUingwood. "As an aid to the teacher they are invaluable,'' GuELPH Mebcuhy. " The style is simple, and adapted to the capacity of cliildren at ■chool." :|i» BEATTY & CLARE'S BbOK-KEEPIHG. A Treatisb on Simolband Double Entry Dook-Keepino,for usb IN High and Public Schools. , By S. G. Beatty, Principal Ontario Commercial Collepe, BellevMe,and Samuel Clare, Book-Keeping and Writing Master, Normal School, Toronto. 3rd Ed., PRICE, 70 CENTS. Authorized by the Minister of Education, Ontario. Authorized by the Chief Supt. Education, Manitoba. Beoommended by the Council ofFublio Instr^iction, Quehee. FROM NOVA SCOTIA AND MANITOBA. A. C. A. DOANE, Insp. P. Schools, Shelburne Co., Nova Scotia. " I have carefully looked over Beatty & Clare's Bookkeeping, and cannot but .-u.mire the simplicity of the outline, the oractical bearing of the transactions, the perspicuity of the instructions, and the varied com- mercial character of the whole work. It commends itself to teachers as a text book and to all others desirous of acquiring a knowledge of this important branch." J. D. McGILLIVRAY, Insp. Schools, Co. Hants., Nova Scotia. Beaty & Clare's Bookkeeping.— " Besides looking over this book myself, I have submitted it to the inspection of practical bookkeepers who agree with me in the propriety of recommending it as a school book. Its directions are minute and to the point, and its examples ample." C. T. ANDREWS, Inspector for Queen's Co., Nova S:otia. "Beatty & Clare's Bookkeepinq has had a careful perusal, with which the principles of bookkeeping are explained and illustrated, vvill recommend this work to any teacher or pupil preparing for examina- tion, while it is sufficiently comprehensive for all practical purposes. L. S. MORSE, M.A., Insp. Schools, Annapolis Co., Nova Scotia. " I have examined Beatty & Clare's Bookkeeping anrt lind it to be an excellent v.'ork. The definitions, forms, and transactvjns therein con- tained, are plain and simple, yet comprehensive and ^iractical. It is well adapted for use in the public schools." D. H. SMITH, A.M., Insp. Schools, Colchester " Beatty & Clare's Bookkeeping is an admirabl' alone is sufficient to secure for the book a place in ou; the Dominion." ova Scotia. 's simplicity . roughout W. S. DANAGH, Inspector for Cnmberland, N. S. a I have looked into Beatty & Clare's Bookkeeping, and have much pleasure in saying that the work is just what is wanted for boys who desire to acquire in a short time such knowledge as will fit them for business*" REV. JOHN AMBROSE, M.A., Supt. of Schools, Digby, N. S. " I am very much pleased with the simplicity and thoroughhess of Beatty & Clare's Bookkeeping. THOS. HART, M.A., Winnipeg. -^ «* Several months ago we introduced Mason's English Grammar into Manitoba College, and now we are introducing Beatty & Clare's Book- keeping. We find them jutt what we oced in their respective subjects." m i A Drill Book for Corrbct and Expressive Kkaoino, Adaptbd KOR THK USB OP Schools, By Richard Lewis, Teacher of Elocution, Author of " Dominion Elocu- tionist," &c. 3rd Ed., Price 75 Cents. m^ Authorized by the Minister of Education frr Ontario. Kj Authorized by the Chief Supt. of Education, Manitoba. I>. H. SMITH, A.M., Inspector of Schools, Colcboster Co., N. 8. " Lewis' ' flovr to Bead,' comes In good time. In no branch of ■tndy Is there more deficiency displayed than in that of reading. Many of our teachers really appear to have no conception as to how reading ahoiild be taught, but by a careful study of Lewis' 'How to liead' they can without any difllculty render themselves fit to give instruction with the utmost satisfaction." L. 8. MOKSE, M.A., Inspector Schools, Annapolis Co., N. S. "Lewis' 'TIow to Read ' treats of a subject which cannot be too highly recommended. Such a work is much needed in our sciiools. The art of rending effectively has been acquired by few teachers, hence they should pruoure this work and thoroughly and practi- cally master the rules and principles therein contained. J. D. McGILLlVEAY, Inspeo*;or of Schools, Co. Hants. - "Lewis' 'ITow to Read,' is the best drill book in elocution for school use that I have seen. I have road it over with a great deal of owe." C. T. ANDREWS, Inspector for Queen's Co., N. S. "I have examined 'How to lload,' and have no hesitation in pronouncing it the best little work on elocution for teachers that hasyetcomo in uler my notice. A thorough drill in the exercises, with due attention to the elementary sounds of the language as illustrated by the author, and an intelligent conception of the principles and suggestions therein given will insure pleasing and expressive reading. It cannot but be hailed with pleasure by every teacher as it Bupplies a want long felt in our schools, and gives to the important Bubjecb of reading its due prominence, as both an art and a science." A. C. A. DOANE, Inspector of Schools, Bhelbnme Co., N. S. " How to Read,' is just what is needed, both as a school class book and an uid to teachers in the proper training of pupils in the principles of effective reading. Rev. JOHN AMBROSE, II.A., Inspector P. Schools, Dlgby, N. S. How TO Read by Richard Le wis.— " This book, for the size of it, is the best by far that I have euer seen on the subject." W. L. DANAGH, Inspector for Cumberland, N. S. "How to Road is a seasonable publication. As a drill book for expressive reading it supplies a desideratum in our schools. It must be admitted that bettov teaching on this branch is greatly needed. The work shows skill and is highly creditable to the author." JOHN Y. GtllM, Broad Cove, Cape Breton, N. S. " The plan pursued in the arrangements of the work, commen- cing with elements essential to correct vocalization, and leading cradually on to principles and practice in some of the piu-est gems of the language, must command itself to every admirer of clear, expressive English reading. The tyrographical ' got up ' of the work is highly creditable to the enterprising iJublishers. f . I? ,;3 li'i \'i c • •M M « • o u 3 •d ^ U cn C • ■t-> CQ 3 ^ ^^ u 2 JS O >** o •k (0 Q «-■ 0) 2 JS < u CO 0i V . ^.J M «i 43 4^ U o o a* Q O 3 ffi O Eh »-> vH o o •s CO «t •d a V S 6 o u 73 •s o o I CANADA SCHOOL JOURNAl Recommended by the Minister of Education in Ontario, Itecemniendcd by the Boord of Education for Quebec, liecommended by the iiupt. of Education, 'New JJrunawicle. "An oxcelleat publication."— Pacific School Journal, Sanfrancisrj. " The Canada School Journal, puhlisliocl by Adam Miller & Co., Toroi is a live educutiouul journal, uud should be in the baudB of every teac)) —titratfoi-d Weekly Herald. EDITORIAL COMMITTEE. J. A. MoLoUan, M.A., LL.D., HiRh School Inspector. Thomaa Kirkland, M.A., Scioiipo Mastor, Normal School. James Hughes, I'ublic School InB])octor, Toronto. Alfred Baker, B.A., Math. Tutor. University College, Toronti PROVINCIAL EDITORS. Ontario— J. M. Buchan, M.A., High School Inspector. G. W. Ross, M.P., Tublic School Inspector. J. C. Glashan, Public School Inspector. Quebec— W. Dale, M.A., Rector High School. S. P. Robins, M.A , Supt. Protestant School, Montreal. New Brunswick— J. Bennett, Ph.D., Supt. City School, Montreal. Nova Scotia— T. C Simunichrast, Registrar, University of Halifax Manitoba— John Canioron, B.A., Winnipeg. British Columbia— John Jessop, Supt. of Fdiication. CONTRIBUTORS. Rev. Fi. Ryerson, D.D., J.L.D., late Chief Supt. of Education. J. G. Hodgins, LL.D., Deputy Minister of Education. Theodore Rand, A.M., D.C.L., Supt. Education, New Brunswick. W. Crocket, A.M., Principal Normal School, Fredericton, N.B. , J. B. Calkin, M.A., Principal Normal School, Trujro, N.S. Dr, Baynw, Halifax High School. Robert Potts, M.A., Cambridge, Eng. Daniel Wilson, LL.D., I'rof. of History and Eng. Lit., Univ. Coll., L Rev. S. S. Nelles, D.D., LL.D., Pros. University Victoria College. Rev. H. G. INIaddock, M.A., F.G.S., Fellow of Clare College, Cambridge, fessor of Classics, Trinity College, Toionto. M. Mo Vicar, Ph.D., LL.D,, Principal State Normal and Training Sch Potsdam, N. Y. Rev. A. F. Kemp, LL.D., Principal Brantford Young Ladies' Ci j Geo. Dickson, B.A., Collegiate Institute, Hamilton. Prof. John A. Macouu, Albert College, Belleville. Rev. Prof. G. M. Meacham, M.A., Numadza, Japan. Wm. Johnson, M.A., Principal Agricultural College, Guelph. John C. McCabe, M.A., Principal Normal School, Ottawa. Dr. S. P. May, Secretary Centennial Education Committee. Prof. J. E. Wells, Canadian Literary Institute, Woodstock. . ; Rev. J. J. Hare, B.A., Ontario Ladies' College, Whitby. ^ James Carlyle, M.D., Math. Master Normal School, To:- >ntQ Geo. Baptie, M.D., Science Master Normal School, Ottawa. f R. Lewis, Teacher of Elocution, Toronto. > Prof. R. Bawson. Belleville. J J. Tilley, Inspector Public Schools, Durham. CANADA SCHOOL JOURNAL IS issued Ist of each month from tho Ofhce of Publication, 11 Welling Street West, Toronto. Subscription i»l per year, payable in advance. ADAM MILLER & CO., Publishers, Toroii; :| JOURNAl ation in Ontario. ■on for Quebec. m, New Brunswick. Journal, Sanfrancisrc. Adam Millor & Co., Toroi the bauds of every teucli ITTEE. 3ctor. al School, ito. tllogo, Toronti TORS. lector. !ctor. )r. jcliool, Montreal. School, Montreal, aivereity of Halifax ation. IS. of Education. ation. , New Brunswick •edericton, N.B. , ruro, N.S. ig. Lit., Univ. Coll., L ■ Victoria College. xre College, Cambridge, £ uito. ormal and Training Sch< L''ouug Ladies' Ci I ton. le. Dan. liege, Guelph. 3l, Ottawa. I Comiriittee. Woodstock. IVhitby. lool. To: vnta )ol, Ottawa. rOURNAL f Publication, 11 Wellingi .LER & CO., Publishers, Toron -.•^ao